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On the existence of solutions to the Navier–Stokes–Poisson equations of a two‐dimensional compressible flow
Author(s) -
Zhang Yinghui,
Tan Zhong
Publication year - 2007
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.786
Subject(s) - barotropic fluid , mathematics , compressibility , poisson distribution , space (punctuation) , flow (mathematics) , compressible flow , navier–stokes equations , mathematical analysis , hagen–poiseuille flow from the navier–stokes equations , poisson's equation , energy (signal processing) , geometry , mechanics , physics , linguistics , statistics , philosophy
In this paper, we consider the Navier–Stokes–Poisson 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)= a ϱlog d (ϱ) for large ϱ. Here d >1 and a >0. Copyright © 2006 John Wiley & Sons, Ltd.