The Pointwise Estimates of Solutions for Euler Equations with Damping in Multi-Dimensions

• DOI: 10.1006/jdeq.2000.3937
• Publication Date: 2002-09-18T10:19:44Z
• Authors: Weike Wang; Tong Yang
• Keywords: Pointwise; Pointwise convergence; Energy method; Constant (computer programming); Euler system; Euler method

We study the time-asymptotic behavior of solutions for the isentropic Euler equations with damping in multi-dimensions. The global existence and pointwise estimates of the solutions are obtained. Furthermore, we obtain the optimal Lp, 1<p⩽+∞, convergence rate of the solution when it is a perturbation of a constant state. Our approach is based on a detailed analysis of the Green function of the linearized system and some energy estimates.