论文标题
某些耗散系统的高级渐近不平等现象
High order asymptotic inequalities for some dissipative systems
论文作者
论文摘要
我们获得了一些重要的基本不平等，这些不平等是根据其$ l^2 $代数衰减的高阶衍生物对某些耗散系统解决方案的长期行为。在文献中，即使对于基本的Navier-Stokes方程也没有观察到其中一些不平等。为了说明这种新方法，我们为不对称不可压缩的流体方程提供了界限，在该方程中，在其中改善了用于微旋转领域的不平等现象。最后，我们展示了如何将该技术应用于其他耗散系统。
We obtain some important fundamental inequalities concerning the long time behavior of high order derivatives for solutions of some dissipative systems in terms of their $L^2$ algebraic decay. Some of these inequalities have not been observed in the literature even for the fundamental Navier-Stokes equations.To illustrate this new approach, we derive bounds for the asymmetric incompressible fluids equations, where an improved inequalities established for the micro-rotational field. Finally, we show how this technique can be applied for other dissipative systems.
