吉首大学学报(自然科学版) ›› 2024, Vol. 45 ›› Issue (1): 13-18.DOI: 10.13438/j.cnki.jdzk.2024.01.003

• 数学 • 上一篇    下一篇

带Navier边界条件的广义随机Navier-Stokes方程解的适定性

薛媛媛,江珊   

  1. (南京财经大学应用数学学院,江苏 南京 210046)
  • 出版日期:2024-01-25 发布日期:2024-01-31
  • 作者简介:薛媛媛(1998—),女,山东德州人,南京财经大学应用数学学院硕士研究生,主要从事随机偏微分方程研究.

Well-Posedness of Generalized Stochastic Navier-Stokes Equation with Navier Boundary Condition

XUE Yuanyuan,JIANG Shan   

  1. (School of Applied Mathematics,Najing University of Finance and Economics,Nanjing 210046,China)
  • Online:2024-01-25 Published:2024-01-31

摘要:对于有界区域二维随机Navier-Stokes方程(有界区域的边界条件为Navier滑移边界条件),给出了该方程弱解在L2L4中的先验估计,证明了非线性项的单调性,并利用经典的Minty-Browder方法证明了方程随机弱解的整体存在性和唯一性.

关键词: Navier滑移边界条件, 阻尼项, 随机Navier-Stokes方程, 适定性

Abstract: For the generalized stochastic Navier-Stokes equations with Navier boundary condition,we prove a priori estimates for the Navier-Stokes equations in L2 and L4.And then,we prove the monotonicity of nonlinear terms.At last by using Minty-Browder we get the global existence and uniqueness for the weak solution of the stochastic equation.

Key words: Navier slip boundary, damping, stochastic Navier-Stokes equation, well-posedness

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