Global existence and large time behavior for the system of compressible adiabatic flow through porous media in ℝ³

2012/11/07 by Guochun Wu Zhong Tan, Jun Huang, Tan, Guochun Wu Zhong +1 · 1 citation
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Computational Fluid Dynamics and Aerodynamics #Navier-Stokes equation solutions #math.AP

paper · pdf · doi:10.48550/arxiv.1211.1613

arxiv created 2012/11/07 · arxiv updated 2012/11/08

Abstract

The system of compressible adiabatic flow through porous media is considered in ℝ³ in the present paper. The global existence and uniqueness of classical solutions are obtained when the initial data is near its equilibrium. We also show that the pressure of the system converges to its equilibrium state at the same L²-rate (1+t)^-3/4 as the Navier-Stokes equations without heat conductivity, but the velocity of the system decays at the L²-rate (1+t)^-5/4, which is faster than the L²-rate (1+t)^-3/4 for the Navier-Stokes equations without heat conductivity [3].

Citations

• The Cauchy problem for quasi-linear symmetric hyperbolic systems

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• Optimal time-decay for Euler-Fourier system with damping in the critical L² framework

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