Tan, Zhong; Wang, Yong Global solution and large-time behavior of the \(3D\) compressible Euler equations with damping. (English) Zbl 1259.35162 J. Differ. Equations 254, No. 4, 1686-1704 (2013). Summary: We construct the global unique solution to the compressible Euler equations with damping in \(R^{3}\). We assume the \(H^{3}\) norm of the initial data is small, but the higher order derivatives can be arbitrarily large. When the \(\Dot{H}^{-s}\) norm \((0\leqslant s< 3/2)\) or \(\dot{B}^{-s}_{2, \infty}\) norm \((0<s\leqslant 3/2)\) of the initial data is finite, by a regularity interpolation trick, we prove the optimal decay rates of the solution. As an immediate byproduct, the \(L^{p}\)-\(L^{2}(1\leqslant p\leqslant 2)\) type of the decay rates follow without requiring that the \(L^{p}\) norm of initial data is small. Cited in 1 ReviewCited in 34 Documents MSC: 35Q31 Euler equations 76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics 35Q35 PDEs in connection with fluid mechanics 35B40 Asymptotic behavior of solutions to PDEs Keywords:Euler equations with damping; global solution; optimal decay rates; interpolation PDFBibTeX XMLCite \textit{Z. Tan} and \textit{Y. Wang}, J. Differ. Equations 254, No. 4, 1686--1704 (2013; Zbl 1259.35162) Full Text: DOI