Free boundary problem for the equation of one-dimensional motion of compressible gas with density-dependent viscosity. (English) Zbl 1027.76042
Summary: We consider a free boundary problem for the equations of one-dimensional isentropic gas motion with density-dependent viscosity \(\mu=b \rho^\beta\), where \(b\) and \(\beta\) are positive constants. We prove that there exists an unique weak solution globally in time, provided that \(\beta< 1/3\).
MSC:
76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
35Q35 | PDEs in connection with fluid mechanics |
35R35 | Free boundary problems for PDEs |