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The pointwise estimates of solutions for Euler equations with damping in multi-dimensions. (English) Zbl 0997.35039

The paper deals with the time-asymptotic behavior of solutions to the isentropic Euler equations with damping in several space dimensions. The main purpose is to study the pointwise estimates of solutions. The case when the solution is a perturbation of a steady state is considered. The analysis is based on some estimates to the solutions by using energy methods, and the estimates of the Green function to the linearized system about the steady state. It is proved that the time-asymptotic shape of the solution is the diffusion wave. The optimal \(L_p\), \(1<p\leq\infty\), convergence rate of the solution is obtained.

MSC:

35Q05 Euler-Poisson-Darboux equations
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35B40 Asymptotic behavior of solutions to PDEs
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