非线性扩散波关于可压缩微极流体方程解的渐近稳定性

Asymptotic Stability of Nonlinear Diffusion Wave Solutions for Compressible Micropolar Fluid Equations

本文研究一维可压缩等熵微极流体方程解的大时间行为,我们证明在初始扰动和波的强度适当小的条件下,当时间时,该方程的解收敛于平面扩散波,并得到了相应的衰减速度,本文主要的研究方法为能量方法,结合了反导数法、Cauchy不等式和Young-不等式证明了非线性扩散波关于可压缩微极流体方程解的渐近稳定性。

In this paper, we study the large time behavior of the solution of one dimensional compressible isentropic micropolar fluid equation. Under the condition of the initial disturbance and wave intensity being appropriately small, at time , we prove that the solution of the equation converges to plane diffusion wave , and the corresponding decay rate is obtained. The main research method in this paper is the energy method, which combines the inverse derivative method, Cauchy inequality and Young inequality. By using these methods, we prove the asymptotic stability of the solution of the nonlinear diffusion wave to the compressible micropolar fluid equation.