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中文摘要：
研究了一类具有与时间相关的黏性系数和黏性热的不定常不可压拟牛顿流问题,即一类不定常热耦合Stokes问题.在一定条件下用Schauder不动点定理证明了弱解的存在性.通过建立弱解对初边值的估计式证明了解的唯一性.给出了有关解的爆破的结论.
英文摘要：
This paper studies an unsteady thermally coupled Stokes problem which describing the unsteady flow of a quasi-Newtonian fluid with temperature-dependent viscosity and with a viscous heating. Existence of a weak solution is proved under some conditions by Schauder＇s fixed point theorem. The estimate of the weak solution which depends on the initial and boundary conditions is established to prove the uniqueness. Result on blowup of the weak solution is also studied.
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