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On the existence of weak solutions to the equations of non‐stationary motion of heat‐conducting incompressible viscous fluids
Author(s) -
Naumann Joachim
Publication year - 2006
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.754
Subject(s) - mathematics , compressibility , regularization (linguistics) , conservation law , viscosity , viscous liquid , weak solution , dissipation , mathematical analysis , term (time) , motion (physics) , momentum (technical analysis) , heat equation , classical mechanics , mechanics , physics , thermodynamics , finance , quantum mechanics , artificial intelligence , computer science , economics
This paper is concerned with the equations of non‐stationary motion in 3D of heat‐conducting incompressible viscous fluids with temperature‐dependent viscosity. The conservation of internal energy includes the usual dissipation term. We prove the existence of a ‘ weak solution with defect measure ’ to the system of PDEs under consideration. Our method of proof is based on a regularization of the equations of conservation of momentum. Copyright © 2006 John Wiley & Sons, Ltd.