Free Boundary Problem for One-Dimensional Motions of Compressible Gas and Vacuum

摘要

We consider a free boundary problem for the equation of one-dimensional isentropic motions with density-dependent viscosity μ = bp~β, where b and 0 are positive constants, when the density function connects to a vacuum continuously on the boundary. We prove that there exists a weak solution globally in time, provided that β < 5/37.