一类随机Navier-Stokes方程弱解的构造

Pub Date : 2014-07-04 DOI:10.1080/17442508.2013.848864

Satoshi Yokoyama

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引用次数: 11

摘要

证明了某变分问题中二维环面上随机Navier-Stokes方程弱解的存在性。我们的方程不满足矫顽力条件。我们构造了它的弱解，由于一个近似的一系列解与扩大粘度项，然后通过显示一个先验估计它们。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Construction of weak solutions of a certain stochastic Navier–Stokes equation

We prove the existence of weak solutions of stochastic Navier–Stokes equation on a two-dimensional torus, which appears in a certain variational problem. Our equation does not satisfy the coercivity condition. We construct its weak solutions due to an approximation by a sequence of solutions of equations with enlarged viscosity terms and then by showing an a priori estimate for them.

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