Hiroshima Mathematical Journal

The initial value problem for motion of incompressible viscous and heat-conductive fluids in Banach spaces

Ryôhei Kakizawa

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.

Article information

Source
Hiroshima Math. J., Volume 40, Number 3 (2010), 371-402.

Dates
First available in Project Euclid: 8 December 2010

https://projecteuclid.org/euclid.hmj/1291818851

Digital Object Identifier
doi:10.32917/hmj/1291818851

Mathematical Reviews number (MathSciNet)
MR2766668

Zentralblatt MATH identifier
1223.35258

Citation

Kakizawa, Ryôhei. The initial value problem for motion of incompressible viscous and heat-conductive fluids in Banach spaces. Hiroshima Math. J. 40 (2010), no. 3, 371--402. doi:10.32917/hmj/1291818851. https://projecteuclid.org/euclid.hmj/1291818851

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