论文标题
玻尔兹曼方程的边界层以三维半空间
Boundary layers of the Boltzmann equation in a three-dimensional half-space
论文作者
论文摘要
在假设Maxwellian的马赫数满足$ {\ cal m} _ {\ infty} <-1 $的情况下，我们通过在麦克斯威尔围绕麦克斯韦的三维半空间来考虑玻尔兹曼方程的非线性边界层。在上述作品中，考虑到固定溶液并确认了非线性稳定性，可以考虑半线玻尔兹曼方程的非线性边界层。在本文中，我们为三维半空间模型建立了固定溶液的独特存在，并表明固定溶液是渐近稳定的。
We consider the nonlinear boundary layers of the Boltzmann equation in a three-dimensional half-space by perturbing around a Maxwellian, under the assumption that the Mach number of the Maxwellian satisfies ${\cal M}_{\infty} < -1$. In preceding works, nonlinear boundary layers of the Boltzmann equation in a half-line are considered, with stationary solutions obtained and nonlinear stability confirmed. In this paper, we establish the unique existence of stationary solutions for the three-dimensional half-space model, and show that the stationary solution is asymptotic stable.
