论文标题
在解决〜广义Navier-Stokes-foury System的解决方案时的指数衰减中
On the exponential decay in time of solutions to a~generalized Navier-Stokes-Fourier system
论文作者
论文摘要
我们考虑一个非牛顿不可压缩的热传导流体，其在边界上的规定不均匀温度，并且具有速度的无滑动边界条件。我们假设没有外部力量。对于像电力法指数的模型一样，在三个维度上大于$ 11/5 $，我们确定了满足熵平等的解决方案，并以适当的指标呈指数融合。实际上，我们显示了该问题的Lyapunov功能。因此，稳定的溶液是非线性稳定的，并吸引了所有合适的弱解决方案。
We consider a non-Newtonian incompressible heat conducting fluid with prescribed nonuniform temperature on the boundary and with the no-slip boundary conditions for the velocity. We assume no external body forces. For the power-law like models with the power law index bigger than $11/5$ in three dimensions, we identify a class of solutions fulfilling the entropy equality and converging to the equilibria exponentially in a proper metric. In fact, we show the existence of a Lyapunov functional for the problem. Consequently, the steady solution is nonlinearly stable and attracts all suitable weak solutions.
