Hiroshima Mathematical Journal

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

Ryôhei Kakizawa

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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

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

First available in Project Euclid: 8 December 2010

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Zentralblatt MATH identifier

Primary: 35Q35: PDEs in connection with fluid mechanics
Secondary: 35K90: Abstract parabolic equations 76D03: Existence, uniqueness, and regularity theory [See also 35Q30]

Incompressible viscous and heat-conductive fluids abstract initial value problem analytic semigroups on Banach spaces


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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