Global regular solutions for 1D degenerate compressible Navier-Stokes equations with large data and far field vacuumr



报告地点:腾讯会议ID:782-541-289 会议密码:1103

报告摘要:For compressible isentropic Navier-Stokes equations, when the viscosity coefficient depends on the density in a sublinear power law, based on an elaborate analysis of the intrinsic singular structure of this degenerate system, we prove the global-in-time well-posedness of regular solutions with conserved total mass, momentum, and finite total energy in some inhomogeneous Sobolev spaces. The key to the proof is the introduction of a well-designed reformulated structure by introducing some new variables and initial compatibility conditions, which, actually, can transfer the degeneracies of the time evolution and the viscosity to the possible singularity of some special source terms. Then, combined with the BD entropy estimates and transport properties of the so-called effective velocity, one can obtain the required uniform a priori estimates of corresponding solutions.