期刊信息
- 刊名： 河北师范大学学报（自然科学版）Journal of Hebei Normal University (Natural Science)
- 主办： 河北师范大学
- ISSN： 1000-5854
- CN： 13-1061/N
- 中国科技核心期刊
- 中国期刊方阵入选期刊
- 中国高校优秀科技期刊
- 华北优秀期刊
- 河北省优秀科技期刊
二维环面上带约束的非自治二维随机Navier-Stokes方程的鞅解
- (河海大学 理学院, 江苏 南京 211100)
-
DOI：10.13763/j.cnki.jhebnu.nse.202301018
Martingale Solutions of Nonautonomous 2D Stochastic Navier-Stokes Equations with Constraint on 2D Torus
摘要/Abstract
研究二维环面上带L2-范数约束的非自治随机 Navier-Stokes 方程鞅解的存在性.首先，利用随机外力中驱动算子的斜对称性和 Galerkin 近似解序列的一致估计，得到近似解分布的 tight 紧性.其次，构造新的概率空间及定义于其上的新随机过程，使得近似解于其上收敛到该随机过程.最后，证明所得新随机过程是原方程的解.同时，得到所得鞅解沿样本轨道唯一，进而得到原方程强解的存在性.
In this paper，we study the existence of martingale solutions for two-dimensional nonautonomous stochastic Navier-Stokes equations with a constraint on the L2-norm of the solution.Firstly，the tightness of laws of approximate solutions is obtained by using the skew-symmetry of the driving operator and uniform estimates of the Galerkin approximate solutions sequence.Secondly，a new probability space and the new stochastic processs defined on it are constructed so that the approximate solutions converge to this new stochastic processs.Finally，we prove that the new stochastic processs is the solution of the original equation.At the same time，we obtain that the martingale solution is unique along the sample orbit，and then obtain the existence of the strong solution of the original equation.