TY - JOUR
T1 - Global Weak Solutions to One-dimensional Compressible Navier-Stokes Equations with Density-dependent Viscosity Coefficients
JO - Journal of Partial Differential Equations
VL - 3
SP - 290
EP - 304
PY - 2010
DA - 2010/08
SN - 23
DO - http://doi.org/10.4208/jpde.v23.n3.6
UR - https://global-sci.org/intro/article_detail/jpde/5235.html
KW - Compressible Navier-Stokes equations
KW - weak solutions
KW - global existence
AB - <p>We prove the global existence of weak solutions of the one-dimensional compressible Navier-stokes equations with density-dependent viscosity. In particular, we assume that the initial density belongs to L^1 and L^∞, module constant states at x=-∞ and x=+∞, which may be different. The initial vacuum is permitted in this paper and the results may apply to the one-dimensional Saint-Venant model for shallow water.</p>