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

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

2011-08-08

arxiv.org/abs/1108.1943v1

Physics

Mathematical Physics

Scientific paper

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 $0< T^* \leq T$.

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