Global weak solutions to the Navier-Stokes equations for a 1D viscous polytropic ideal gas

Authors:
Song Jiang and Ping Zhang

Journal:
Quart. Appl. Math. **61** (2003), 435-449

MSC:
Primary 76N10; Secondary 35L65, 35Q30

DOI:
https://doi.org/10.1090/qam/1999830

MathSciNet review:
MR1999830

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Abstract: We prove the existence of global weak solutions to the Navier-Stokes equations for a one-dimensional viscous polytropic ideal gas. We require only that the initial density is in with positive infimum, the initial velocity is in , and the initial temperature is in with positive infimum. The initial density and the initial velocity may have differing constant states at . In particular, piecewise constant data with arbitrary large jump discontinuities are included. Our results show that neither vacuum states nor concentration states can form and the temperature remains positive in finite time.

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DOI:
https://doi.org/10.1090/qam/1999830

Article copyright:
© Copyright 2003
American Mathematical Society