论文标题
随机对流Brinkman-Forchheimer方程的渐近对数 - 习惯不平等
Asymptotic log-Harnack inequality for the stochastic convective Brinkman-Forchheimer equations with degenerate noise
论文作者
论文摘要
在这项工作中，我们考虑了两个和三维随机的对流Brinkman-Forchheimer（SCBF）方程，并检查其强大解决方案的一些渐近行为。我们为通过渐近偶联方法建立了与由添加剂和乘法变性噪声驱动的SCBF方程相关的过渡半群的渐近对数 - 摩nack不平等。作为渐近对数 - 摩纳克不平等现象的应用，我们得出了梯度估计，渐近不可还原性，渐近强的霉菌特性，渐近热内核估计和真实性。每当（3，\ infty）$中的吸收指数$ r \时，就会获得渐近日志不平等现象，而无需限制Brinkman系数（有效粘度）$μ> 0 $，DARCY系数$ a> 0 $ 0 $ 0 $和FORCHHEIMER系数$ $ beby $ bebeby $ bebeby $ bebebeby $ beby $ beby $ beb。
In this work, we consider the two and three dimensional stochastic convective Brinkman-Forchheimer (SCBF) equations and examine some asymptotic behaviors of its strong solution. We establish the asymptotic log-Harnack inequality for the transition semigroup associated with the SCBF equations driven by additive as well as multiplicative degenerate noise via the asymptotic coupling method. As applications of the asymptotic log-Harnack inequality, we derive the gradient estimate, asymptotic irreducibility, asymptotic strong Feller property, asymptotic heat kernel estimate and ergodicity. Whenever the absorption exponent $r\in(3,\infty)$, the asymptotic log-Harnack inequality is obtained without any restriction on the Brinkman coefficient (effective viscosity) $μ>0$, the Darcy coefficient $α>0$ and the Forchheimer coefficient $β>0$.
