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Volume 23, Issue 3
Global Weak Solutions to One-dimensional Compressible Navier-Stokes Equations with Density-dependent Viscosity Coefficients

Wuming Li & Quansen Jiu

DOI: 10.4208/jpde.v23.n3.6

J. Part. Diff. Eq., 23 (2010), pp. 290-304.

Published online: 2010-08

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  • Abstract

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.

  • Keywords

Compressible Navier-Stokes equations weak solutions global existence

  • AMS Subject Headings

35D05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-23-290, author = {}, title = {Global Weak Solutions to One-dimensional Compressible Navier-Stokes Equations with Density-dependent Viscosity Coefficients}, journal = {Journal of Partial Differential Equations}, year = {2010}, volume = {23}, number = {3}, pages = {290--304}, abstract = {

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.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v23.n3.6}, url = {http://global-sci.org/intro/article_detail/jpde/5235.html} }
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 -

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.

Wuming Li & Quansen Jiu . (2019). Global Weak Solutions to One-dimensional Compressible Navier-Stokes Equations with Density-dependent Viscosity Coefficients. Journal of Partial Differential Equations. 23 (3). 290-304. doi:10.4208/jpde.v23.n3.6
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