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学者姓名：江飞
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Abstract ：
We study the existence of unstable classical solutions of the Rayleigh-Taylor instability problem (abbr. RT problem) of an inhomogeneous incompressible viscous fluid in a bounded domain. We find that, by using an existence theory of (steady) Stokes problem and an iterative technique, the initial data of classical solutions of the linearized RT problem can be modified to new initial data, which can generate local-in-time classical solutions of the RT problem, and are close to the original initial data. Thus, we can use a classical bootstrap instability method to further obtain classical solutions of (nonlinear) RT instability based on the ones of linear RT instability.
Keyword ：
35B10 35B10 35M33 35M33 35Q35 35Q35 76D05 76D05 76E25 76E25
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| GB/T 7714 | Jiang, Fei , Zhao, Youyi . Classical Solutions of Rayleigh-Taylor instability for inhomogeneous incompressible viscous fluids in bounded domains [J]. | CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS , 2024 , 63 (4) . |
| MLA | Jiang, Fei 等. "Classical Solutions of Rayleigh-Taylor instability for inhomogeneous incompressible viscous fluids in bounded domains" . | CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS 63 . 4 (2024) . |
| APA | Jiang, Fei , Zhao, Youyi . Classical Solutions of Rayleigh-Taylor instability for inhomogeneous incompressible viscous fluids in bounded domains . | CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS , 2024 , 63 (4) . |
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Abstract ：
Motivated by the stability result of the Rayleigh-Benard problem in a fixed slab domain in Jiang and Liu (Nonlinearity 33:1677-1704, 2020) and the global-in-time well-posedness of an incompressible viscoelastic fluid system with an upper free boundary in Xu et al. (Arch Ration Mech Anal 208:753-803, 2013), we further investigate the Rayleigh-Benard problem for an incompressible viscoelastic fluid in a three-dimensional horizontally periodic domain with the lower fixed boundary and with the upper free boundary. By a careful energy method, we establish an explicit stability condition, under which the viscoelastic Rayleigh- Benard problem has a unique global-in-time solution with exponential time-decay. Our result presents that the elasticity can inhibit the thermal instability for sufficiently large elasticity coefficient kappa.
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| GB/T 7714 | Jiang, Fei , Liu, Mengmeng , Zhao, Youyi . Stability of the viscoelastic Rayleigh-Benard problem with an upper free boundary [J]. | CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS , 2023 , 62 (3) . |
| MLA | Jiang, Fei 等. "Stability of the viscoelastic Rayleigh-Benard problem with an upper free boundary" . | CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS 62 . 3 (2023) . |
| APA | Jiang, Fei , Liu, Mengmeng , Zhao, Youyi . Stability of the viscoelastic Rayleigh-Benard problem with an upper free boundary . | CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS , 2023 , 62 (3) . |
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This paper is mainly concerned with the global existence and asymptotic behaviour of classical solutions to the three-dimensional (3D) incompressible non-resistive viscous magnetohydrodynamic (MHD) equations with large initial perturbations in a 3D periodic domain (in Lagrangian coordinates). Motivated by the approximate theory of the ideal MHD equations in Bardos et al. (Trans Am Math Soc 305:175-191, 1988), the Diophantine condition imposed in Chen et al. (Sci China Math 64:1-10, 2021) and the magnetic inhibition mechanism in the version of Lagrangian coordinates analyzed in Jiang and Jiang (Arch Ration Mech Anal 233:749-798, 2019), we prove the global existence of a unique classical solution with some class of large initial perturbations, where the intensity of impressed magnetic fields depends increasingly on the H17xH21-norm of the initial velocity and magnetic field perturbations. Our result not only mathematically verifies that a strong impressed magnetic field can prevent the singularity formation of classical solutions with large initial data in the viscous MHD case, but also provides a starting point for the existence theory of large perturbation solutions to the 3D non-resistive viscous MHD equations. In addition, we also show that for large time or sufficiently strong impressed magnetic fields, the MHD equations converge to the corresponding linearized pressureless equations in the algebraic convergence-rates with respect to both time and field intensity.
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| GB/T 7714 | Jiang, Fei , Jiang, Song . On Magnetic Inhibition Theory in 3D Non-resistive Magnetohydrodynamic Fluids: Global Existence of Large Solutions [J]. | ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS , 2023 , 247 (5) . |
| MLA | Jiang, Fei 等. "On Magnetic Inhibition Theory in 3D Non-resistive Magnetohydrodynamic Fluids: Global Existence of Large Solutions" . | ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS 247 . 5 (2023) . |
| APA | Jiang, Fei , Jiang, Song . On Magnetic Inhibition Theory in 3D Non-resistive Magnetohydrodynamic Fluids: Global Existence of Large Solutions . | ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS , 2023 , 247 (5) . |
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It is still open whether the inhibition phenomenon of the Rayleigh-Taylor (RT) instability by a horizontal magnetic field can be mathematically verified for a non-resistive magnetohydrodynamic (MHD) fluid in a two-dimensional (2D) horizontal slab domain, since it was roughly verified in the linearized case by Wang in [43]. In this paper, we show that this inhibition phenomenon can be rigorously verified in the (nonlinear) inhomogeneous, incompressible, inviscid case with velocity damping. More precisely, we show that there is a critical number mC, such that if the strength |m| of a horizontal magnetic field is bigger than mC, then the small perturbation solution around the magnetic RT equilibrium state is exponentially stable in time. Moreover, we also provide a nonlinear instability result for the case |m| is an element of (0, mC). Our instability result reveals that a horizontal magnetic field can not inhibit the RT instability, if it's strength is too small. (c) 2022 Elsevier Inc. All rights reserved.
Keyword ：
Exponential stability Exponential stability Ideal MHD fluids Ideal MHD fluids Non-resistive inviscid fluid Non-resistive inviscid fluid Rayleigh-Taylor instability Rayleigh-Taylor instability Velocity damping Velocity damping
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| GB/T 7714 | Jiang, Fei , Jiang, Song , Zhao, Youyi . On inhibition of the Rayleigh-Taylor instability by a horizontal magnetic field in ideal MHD fluids with velocity damping [J]. | JOURNAL OF DIFFERENTIAL EQUATIONS , 2022 , 314 : 574-652 . |
| MLA | Jiang, Fei 等. "On inhibition of the Rayleigh-Taylor instability by a horizontal magnetic field in ideal MHD fluids with velocity damping" . | JOURNAL OF DIFFERENTIAL EQUATIONS 314 (2022) : 574-652 . |
| APA | Jiang, Fei , Jiang, Song , Zhao, Youyi . On inhibition of the Rayleigh-Taylor instability by a horizontal magnetic field in ideal MHD fluids with velocity damping . | JOURNAL OF DIFFERENTIAL EQUATIONS , 2022 , 314 , 574-652 . |
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Abstract ：
We consider the magnetic Benard problem for a horizontal layer of inviscid, thermally and electrically conducting fluid, and prove that the thermal convection is inhibited by a strong enough uniform vertical magnetic field. The key ingredient here is to use a new representation of the vertical component of the velocity, derived from the magnetic equations due to the transversality of the magnetic field, to control the thermal instability. This works also for the classical viscous magnetic Benard problem, which in particular improves the result of Galdi (Arch Ration Mech Anal 62(2):167-186, 1985) in the large Chandrasekhar number limit and justifies, in the nonlinear sense, the theory in Chandrasekhar (Hydrodynamic and Hydromagnetic Stability. The International Series of Monographs on Physics, Clarendon Press, Oxford, 1961) that the temperature gradient for the onset of convection is independent of the viscosity in this limit.
Keyword ：
Benard problem Benard problem Magnetic inhibition Magnetic inhibition Magnetohydrodynamics Magnetohydrodynamics Nonlinear stability Nonlinear stability Thermal convection Thermal convection
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| GB/T 7714 | Jiang, Fei , Wang, Yanjin . Nonlinear Stability of the Inviscid Magnetic Benard Problem [J]. | JOURNAL OF MATHEMATICAL FLUID MECHANICS , 2022 , 24 (4) . |
| MLA | Jiang, Fei 等. "Nonlinear Stability of the Inviscid Magnetic Benard Problem" . | JOURNAL OF MATHEMATICAL FLUID MECHANICS 24 . 4 (2022) . |
| APA | Jiang, Fei , Wang, Yanjin . Nonlinear Stability of the Inviscid Magnetic Benard Problem . | JOURNAL OF MATHEMATICAL FLUID MECHANICS , 2022 , 24 (4) . |
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The global existence of small smooth solutions to the equations of two-dimensional incompressible, inviscid, nonresistive magnetohydrodynamic (MHD) fluids with velocity damping has been established in [J. H. Wu, Y. F. Wu, and X. J. Xu, SIAM J. Math. Anal., 47 (2015), pp. 2630-2656]. In this paper we further study the global existence for an initial-boundary value problem in a horizontally periodic domain with finite height in three dimensions. Motivated by the multilayer energy method introduced in [Y. Guo and I. Tice, Arch. Ration. Mech. Anal., 207 (2013), pp. 459-531], we develop a new type of two-layer energy structure to overcome the difficulties arising from three-dimensional nonlinear terms in the MHD equations, and prove thus the initial-boundary value problem admits a unique global smooth solution with small initial data. Moreover, the solution decays exponentially in time to some rest state. Our two-layer energy structure enjoys two features: (1) the lower-order energy (functional) cannot be controlled by the higher-order energy; (2) under the a priori smallness assumption of the lower-order energy, we can first close the higher-order energy estimates, and then further close the lower-energy estimates in turn.
Keyword ：
damping damping exponential decay exponential decay global well-posedness global well-posedness incompressible incompressible inviscid inviscid nonresistive MHD fluids nonresistive MHD fluids
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| GB/T 7714 | Jiang, Fei , Jiang, Song , Zhao, Youyi . GLOBAL SOLUTIONS OF THE THREE-DIMENSIONAL INCOMPRESSIBLE IDEAL MHD EQUATIONS WITH VELOCITY DAMPING IN HORIZONTALLY PERIODIC DOMAINS [J]. | SIAM JOURNAL ON MATHEMATICAL ANALYSIS , 2022 , 54 (4) : 4891-4929 . |
| MLA | Jiang, Fei 等. "GLOBAL SOLUTIONS OF THE THREE-DIMENSIONAL INCOMPRESSIBLE IDEAL MHD EQUATIONS WITH VELOCITY DAMPING IN HORIZONTALLY PERIODIC DOMAINS" . | SIAM JOURNAL ON MATHEMATICAL ANALYSIS 54 . 4 (2022) : 4891-4929 . |
| APA | Jiang, Fei , Jiang, Song , Zhao, Youyi . GLOBAL SOLUTIONS OF THE THREE-DIMENSIONAL INCOMPRESSIBLE IDEAL MHD EQUATIONS WITH VELOCITY DAMPING IN HORIZONTALLY PERIODIC DOMAINS . | SIAM JOURNAL ON MATHEMATICAL ANALYSIS , 2022 , 54 (4) , 4891-4929 . |
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We study the existence and uniqueness of global strong solutions to the equations of an incompressible viscoelastic fluid in a spatially periodic domain, and show that a unique strong solution exists globally in time if the initial deformation and velocity are small for the given physical parameters. In particular, the initial velocity can be large for the large elasticity coefficient. Our result mathematically verifies that the elasticity can prevent the formation of singularities of strong solutions with large initial velocity, thus playing a similar role to viscosity in preventing the formation of singularities in viscous flows. Moreover, for given initial velocity perturbation and zero initial deformation around the rest state, we find, as the elasticity coefficient or time goes toinfinity, that (1) any straight line segment l(0)consisted of fluid particles in the rest state, after being bent by a velocity perturbation, will turn into a straight line segment that is parallel to l(0)and has the same length as l(0). (2) the motion of the viscoelastic fluid can be approximated by a linear pressureless motion in Lagrangian coordinates, even when the initial velocity is large. Moreover, the above mentioned phenomena can also be found in the corresponding compressible fluid case. (C)2021 Elsevier Inc. All rights reserved.
Keyword ：
Elasticity coefficient Elasticity coefficient Exponential stability Exponential stability Incompressible/compressible viscoelastic flows Incompressible/compressible viscoelastic flows Strong solutions Strong solutions
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| GB/T 7714 | Jiang, Fei , Jiang, Song . Strong solutions of the equations for viscoelastic fluids in some classes of large data [J]. | JOURNAL OF DIFFERENTIAL EQUATIONS , 2021 , 282 : 148-183 . |
| MLA | Jiang, Fei 等. "Strong solutions of the equations for viscoelastic fluids in some classes of large data" . | JOURNAL OF DIFFERENTIAL EQUATIONS 282 (2021) : 148-183 . |
| APA | Jiang, Fei , Jiang, Song . Strong solutions of the equations for viscoelastic fluids in some classes of large data . | JOURNAL OF DIFFERENTIAL EQUATIONS , 2021 , 282 , 148-183 . |
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It is well-known that viscoelasticity is a material property that exhibits both viscous and elastic characteristics with deformation. In particular, an elastic fluid strains when it is stretched and quickly returns to its original state once the stress is removed. In this review, we first introduce some mathematical results, which exhibit the stabilizing effect of elasticity on the motion of viscoelastic fluids. Then we further briefly introduce similar stabilizing effect in the elastic fluids.
Keyword ：
elastic fluids elastic fluids viscoelastic fluids viscoelastic fluids viscoelastic Rayleigh-Benard problem viscoelastic Rayleigh-Benard problem Viscoelastic Rayleigh-Taylor problem Viscoelastic Rayleigh-Taylor problem
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| GB/T 7714 | Jiang, Fei . STABILIZING EFFECT OF ELASTICITY ON THE MOTION OF VISCOELASTIC/ELASTIC FLUIDS [J]. | ELECTRONIC RESEARCH ARCHIVE , 2021 , 29 (6) : 4051-4074 . |
| MLA | Jiang, Fei . "STABILIZING EFFECT OF ELASTICITY ON THE MOTION OF VISCOELASTIC/ELASTIC FLUIDS" . | ELECTRONIC RESEARCH ARCHIVE 29 . 6 (2021) : 4051-4074 . |
| APA | Jiang, Fei . STABILIZING EFFECT OF ELASTICITY ON THE MOTION OF VISCOELASTIC/ELASTIC FLUIDS . | ELECTRONIC RESEARCH ARCHIVE , 2021 , 29 (6) , 4051-4074 . |
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We investigate the stability and instability of the magnetic Rayleigh-Benard problem with zero resistivity. A stability criterion is established, under which the magnetic Benard problem is stable. The proof is mainly based on a three-layers energy method and an idea of magnetic inhibition mechanism. The stability result first mathematically verifies Chandrasekhar's physical conjecture in 1955 that the thermal instability can be inhibited by a strong (impressed) magnetic field in magnetohydrodynamic (MHD) fluids with zero resistivity (based on a linearized steady magnetic Benard equations). In addition, we also provide an instability criterion, under which the magnetic Rayleigh-Benard problem is unstable. The instability proof is mainly based on a bootstrap instability method by further developing new techniques. Our instability result shows that the thermal instability still occurs when the (impressed) magnetic field is weak. (C) 2020 Elsevier Masson SAS. All rights reserved.
Keyword ：
Magnetohydrodynamic fluid Magnetohydrodynamic fluid Rayleigh-Benard problem Rayleigh-Benard problem Stability Stability Thermal instability Thermal instability
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| GB/T 7714 | Jiang, Fei , Jiang, Song . On inhibition of thermal convection instability by a magnetic field under zero resistivity [J]. | JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES , 2020 , 141 : 220-265 . |
| MLA | Jiang, Fei 等. "On inhibition of thermal convection instability by a magnetic field under zero resistivity" . | JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES 141 (2020) : 220-265 . |
| APA | Jiang, Fei , Jiang, Song . On inhibition of thermal convection instability by a magnetic field under zero resistivity . | JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES , 2020 , 141 , 220-265 . |
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We choose a constitutive model, which consists of a viscous stress component and a stress component for a neo-Hookean solid, to describe the motion of a viscoelastic fluid heated from below, and then mathematically investigate the stability for the Rayleigh-Benard problem of the constitutive model. A stability criterion is established, under which the Rayleigh-Benard problem is exponentially stable with respect to time. Our stability result shows that the elasticity can inhibit the thermal instability under sufficiently large elasticity coefficient . In addition, we also provide an instability criterion, under which the Rayleigh-Benard problem is unstable. Our instability result shows that elasticity can not inhibit the thermal instability, when is too small.
Keyword ：
incompressible viscoelastic fluids incompressible viscoelastic fluids Rayleigh-Benard problem Rayleigh-Benard problem stability stability thermal instability thermal instability
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| GB/T 7714 | Jiang, Fei , Liu, Mengmeng . Nonlinear stability of the viscoelastic Benard problem [J]. | NONLINEARITY , 2020 , 33 (4) : 1677-1704 . |
| MLA | Jiang, Fei 等. "Nonlinear stability of the viscoelastic Benard problem" . | NONLINEARITY 33 . 4 (2020) : 1677-1704 . |
| APA | Jiang, Fei , Liu, Mengmeng . Nonlinear stability of the viscoelastic Benard problem . | NONLINEARITY , 2020 , 33 (4) , 1677-1704 . |
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