The initial value problem for the heat convection equations with the dissipation in Banach spaces
نویسنده
چکیده
We consider the abstract initial value problem for evolution equations which describe heat convection of incompressible viscous fluids. It is difficulty that we do not neglect the dissipation function in contrast to the Boussinesq approximation. This problem has uniquely a mild solution. 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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