Global Solutions to the Gas-Vacuum Interface Problem of Isentropic Compressible Inviscid Flows with Damping in Spherically Symmetric Motions and Physical Vacuum

Abstract

For the physical vacuum free boundary problem with the sound speed being $C^{1/2}$-H$\ddot{\mathrm{o}}$lder continuous near vacuum boundaries of the three-dimensional compressible Euler equations with damping, the global existence of spherically symmetric smooth solutions is proved, which are shown to converge to Barenblatt self-similar solutions of the porous media equation with the same total masses when initial data are small perturbations of Barenblatt solutions. The pointwise convergence with a rate of density, the convergence rate of velocity in supreme norm and the precise expanding rate of physical vacuum boundaries are also given by constructing nonlinear functionals with space-time weights featuring the behavior of solutions in large time and near the vacuum boundary and the center of symmetry, the nonlinear energy estimates and elliptic estimates.

arXiv admin note: substantial text overlap with arXiv:1407.6111

References in corpus (1)

• Local Well-posedness of the three dimensional compressible Euler--Poisson equations with physical vacuum