论文标题
关于通用的Navier-Stokes-toury系统实现熵平等的解决方案
On solutions for a generalized Navier-Stokes-Fourier system fulfilling entropy equality
论文作者
论文摘要
我们考虑在速度场的均匀dirichlet边界条件和温度下的空间不均匀的dirichlet边界条件下，在受均匀的dirichlet边界条件下进行的有界域中的非牛顿热传导不可压缩流体的流动。最终目标是表明随着时间的时间趋于无限，流体会收敛到平衡。但是，为了证明这种结果是合理的，需要处理非常特殊的不平等和非常特殊的测试功能，这些功能通常在弱解决方案水平上不可允许。在本文中，我们展示了如何克服这种困难。特别是，我们显示了满足熵平等的解决方案的存在，这似乎是应研究稳定性结果的最佳解决方案类别。
We consider a flow of non-Newtonian heat conducting incompressible fluid in a bounded domain subjected to the homogeneous Dirichlet boundary condition for the velocity field and the spatially inhomogeneous Dirichlet boundary condition for the temperature. The ultimate goal is to show that the fluid converges to equilibrium as time tends to infinity. However, to justify such result, one needs to deal with very special inequalities and very special test functions, which are typically not admissible on the level of weak solutions. In this paper, we show how one can overcome such difficulties. In particular, we show the existence of a solution fulfilling the entropy equality, which seems to be optimal class of solutions in which one should study the stability result.
