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November 2010 The initial value problem for motion of incompressible viscous and heat-conductive fluids in Banach spaces
Ryôhei Kakizawa
Hiroshima Math. J. 40(3): 371-402 (November 2010). DOI: 10.32917/hmj/1291818851

Abstract

We consider the abstract initial value problem for the system of evolution equations which describe motion of incompressible viscous and heat-conductive fluids in a bounded domain. It is difficulty of our problem that we do not neglect the viscous dissipation function in contrast to the Boussinesq approximation. This problem has uniquely a mild solution locally in time for general initial data, and globally in time for small initial data. Moreover, a mild solution of this problem can be a strong or classical solution under appropriate assumptions for initial data. We prove the above properties by the theory of analytic semigroups on Banach spaces.

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Ryôhei Kakizawa. "The initial value problem for motion of incompressible viscous and heat-conductive fluids in Banach spaces." Hiroshima Math. J. 40 (3) 371 - 402, November 2010. https://doi.org/10.32917/hmj/1291818851

Information

Published: November 2010
First available in Project Euclid: 8 December 2010

zbMATH: 1223.35258
MathSciNet: MR2766668
Digital Object Identifier: 10.32917/hmj/1291818851

Subjects:
Primary: 35Q35
Secondary: 35K90, 76D03

Rights: Copyright © 2010 Hiroshima University, Mathematics Program

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Vol.40 • No. 3 • November 2010
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