Hiroshima Mathematical Journal
- Hiroshima Math. J.
- Volume 40, Number 3 (2010), 371-402.
The initial value problem for motion of incompressible viscous and heat-conductive fluids in Banach spaces
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.
Hiroshima Math. J., Volume 40, Number 3 (2010), 371-402.
First available in Project Euclid: 8 December 2010
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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