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On the existence of solutions to the Navier–Stokes equations of a two‐dimensional compressible flow
Author(s) -
Erban Radek
Publication year - 2003
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.362
Subject(s) - barotropic fluid , mathematics , compressibility , navier–stokes equations , flow (mathematics) , space (punctuation) , compressible flow , mathematical analysis , energy (signal processing) , hagen–poiseuille flow from the navier–stokes equations , geometry , mechanics , physics , linguistics , statistics , philosophy
We consider the Navier–Stokes equations for compressible, barotropic flow in two space dimensions. We introduce useful tools from the theory of Orlicz spaces. Then we prove the existence of globally defined finite energy weak solutions for the pressure satisfying p ( ϱ ) = aϱ log d ( ϱ ) for large ϱ . Here d >1 and a > 0. Copyright © 2003 John Wiley & Sons, Ltd.