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Smooth Solution of the Compressible Navier–Stokes Equations in an Unbounded Domain with Inflow Boundary Condition

✍ Scribed by Jae Ryong Kweon; R.Bruce Kellogg

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
213 KB
Volume
220
Category
Article
ISSN
0022-247X

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✦ Synopsis

The barotropic compressible Navier᎐Stokes equations in an unbounded domain Ž . Ž . are studied. We prove the unique existence of the solution u, p of the system 1.1 in the Sobolev space H kq 3 = H kq 2 provided that the derivatives of the data of the problem are sufficiently small, where k G 0 is any integer. The proof follows from an analysis of the linearized problem, the solvability of the continuity equation, and the Schauder fixed point theory. Similar smoothness results are obtained for a Ž . linearized form of 1.1 .

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