Pointwise wave behavior of the Navier-Stokes equations in half space

In this paper, we investigate the pointwise behavior of the solution for the compressible Navier-Stokes equations with mixed boundary condition in half space. Our results show that the leading order of Green's function for the linear system in half space are heat kernels propagating with sound...

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Bibliographic Details
Published inarXiv.org
Main Authors Du, Linglong, Wang, Haitao
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 27.09.2017
Subjects
Boundary conditions
Compressibility
Decay rate
Diffusion waves
Fluid dynamics
Fluid flow
Green's functions
Kernels
Mathematical analysis
Navier-Stokes equations
Nonlinear analysis
Sound
Sound propagation
Wave interaction
Wave propagation
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Summary:In this paper, we investigate the pointwise behavior of the solution for the compressible Navier-Stokes equations with mixed boundary condition in half space. Our results show that the leading order of Green's function for the linear system in half space are heat kernels propagating with sound speed in two opposite directions and reflected heat kernel (due to the boundary effect) propagating with positive sound speed. With the strong wave interactions, the nonlinear analysis exhibits the rich wave structure: the diffusion waves interact with each other and consequently, the solution decays with algebraic rate.
ISSN:2331-8422