标题： 非定常通道中导热粘性不可压缩流体的强解与耗散加热 显示英文标题

标题： Strong Solutions to Non-Stationary Channel Flows of Heat-Conducting Viscous Incompressible Fluids with Dissipative Heating

摘要： 我们研究了一个在时间区间 $(0,T)$上的通道状区域中，随时间变化的导热粘性不可压缩流体的初边值问题。 对于包含强非线性和人工（所谓“什么也不做”）边界条件的抛物型系统，我们证明了解在时间区间 $(0,T^*)$上局部存在、全局唯一且光滑，其中 $0< T^* \leq T$。 显示英文摘要

摘要： We study an initial-boundary-value problem for time-dependent flows of heat-conducting viscous incompressible fluids in channel-like domains on a time interval $(0,T)$. For the parabolic system with strong nonlinearities and including the artificial (the so called "do nothing") boundary conditions, we prove the local in time existence, global uniqueness and smoothness of the solution on a time interval $(0,T^*)$, where $0< T^* \leq T$.