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Global solutions of the Navier–Stokes equations for viscous compressible flows

✍ Scribed by Dehua Wang

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
229 KB
Volume
52
Category
Article
ISSN
0362-546X

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✦ Synopsis

The compressible Navier-Stokes equations for viscous ows with general large continuous initial data, as well as with large discontinuous initial data, are studied. Both a homogeneous free boundary problem with zero outer pressure and a ÿxed boundary problem are considered. For the large initial data in H 1 , the existence, uniqueness, and regularity of global solutions in H 1 for real viscous ows are established, and it is showed that neither shock waves nor vacuum and concentration in the solutions are developed in a ÿnite time. For the large discontinuous data, the global existence of large weak solutions for the perfect gases is also established using a di erent argument, and it is indicated that the solutions do not develop vacuum or concentration although the solutions have large discontinuity. For the free boundary problem, the interface separating the ows from the zero outer pressure expands at a ÿnite speed.

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