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学者姓名：赵友义
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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 ：
The inhibition phenomenon of Rayleigh-Taylor instability by surface tension in stratified incompressible viscous fluids driven by gravity has been established in [Y.J. Wang, I. Tice and C. Kim, Arch. Ration. Mech. Anal., 212 (2014), pp. 1-92] via a special flattening coordinate transformation. However, it remains an open problem whether this inhibition phenomenon can be rigorously verified in Lagrangian coordinates due to the delicate nonlinear part of the surface tension term. In this paper, we provide a new mathematical approach, together with some key observations, to prove that the Rayleigh-Taylor problem in Lagrangian coordinates admits a unique global -intime solution under the sharp stability condition nu > nu(C), where nu and nu(C) are the surface tension coefficient and the threshold of the surface tension coefficient, respectively. Furthermore, the solution decays exponentially in time to the equilibrium. Our result provides a rigorous proof of the inhibition phenomenon of Rayleigh-Taylor instability by surface tension under Lagrangian coordinates.
Keyword ：
incompressible viscous fluids incompressible viscous fluids inhibiting effect inhibiting effect Lagrangian coordinates Lagrangian coordinates Rayleigh-Taylor instability Rayleigh-Taylor instability stratified fluids stratified fluids surface tension surface tension
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| GB/T 7714 | Zhao, Youyi . ON THE INHIBITION OF RAYLEIGH-TAYLOR INSTABILITY BY SURFACE TENSION IN STRATIFIED INCOMPRESSIBLE VISCOUS FLUIDS UNDER LAGRANGIAN COORDINATES [J]. | DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS , 2024 , 44 (9) : 2815-2845 . |
| MLA | Zhao, Youyi . "ON THE INHIBITION OF RAYLEIGH-TAYLOR INSTABILITY BY SURFACE TENSION IN STRATIFIED INCOMPRESSIBLE VISCOUS FLUIDS UNDER LAGRANGIAN COORDINATES" . | DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS 44 . 9 (2024) : 2815-2845 . |
| APA | Zhao, Youyi . ON THE INHIBITION OF RAYLEIGH-TAYLOR INSTABILITY BY SURFACE TENSION IN STRATIFIED INCOMPRESSIBLE VISCOUS FLUIDS UNDER LAGRANGIAN COORDINATES . | DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS , 2024 , 44 (9) , 2815-2845 . |
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