巴拿赫空间中热传导微极流体运动的初值问题
The initial value problem for motion of micropolar fluids with heat conduction in Banach spaces
摘要：
考虑有界区域内微极流体运动的发展方程系统的抽象初值问题。对于一般的初始数据，该问题在时间上局部有唯一的温和解，而对于小的初始数据，该问题在时间上全局有唯一的温和解。此外，在对初始数据的适当假设下，该问题的温和解可以是强解或经典解。我们利用巴拿赫空间上的解析半群理论证明了上述性质。
英文摘要：
We consider the abstract initial value problem for the system of evolution equations which describe motion of micropolar fluids with heat conduction in a bounded domain. 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.
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