The initial value problem for the heat convection equations of asymmetric fluids in Banach spaces

We consider the abstract initial value problem for evolution equations which describe heat convection of incompressible viscous isotropic fluids with the asymmetric stress tensor. It is difficulty in the law of conservation of energy that the dissipation function must be taken into account. 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.