跳噪声扰动下人工压缩Navier-Stokes方程解的适定性

doi:10.13438/j.cnki.jdzk.2022.02.003

吉首大学学报（自然科学版） ›› 2022, Vol. 43 ›› Issue (2): 11-16.DOI: 10.13438/j.cnki.jdzk.2022.02.003

跳噪声扰动下人工压缩Navier-Stokes方程解的适定性

张芳

（南京财经大学应用数学学院，江苏南京 210046）

出版日期:2022-03-25 发布日期:2022-07-14
作者简介:张芳(1996—)，女，安徽滁州人，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.
基金资助:
国家自然科学基金资助项目(11701269)

Well-Posedness of Solutions of Artificially Compressed Navier Stokes Equations with Jump Noise

ZHANG Fang

(School of Applied Mathematics,Nanjing University of Finance and Economics,Nanjing 210046,China)

Online:2022-03-25 Published:2022-07-14

摘要/Abstract

摘要：为了克服不可压约束条件数值计算困难，引入人工压缩方法，利用Lévy型伊藤公式、一致先验估计、局部单调性和弱收敛方法，由经典的Minty-Browder方法得到人工压缩Navier-Stokes方程强解的存在唯一性.

关键词： 跳噪声, 人工压缩Navier-Stokes方程, 存在唯一性, Minty-Browder方法

Abstract: For the difficulty of numerical calculation under incompressible constraints,the artificial compression method is introduced.With Lévy It formula,uniform a priori estimation,local monotonicity and weak convergence method,the existence and uniqueness of strong solutions of the artificial compression Navier- Stokes equation is obtained by the classical Minty-Browder method.

Key words: jump noise, artificial compression Navier Stokes equation, existence and uniqueness, Minty-Browder method

张芳. 跳噪声扰动下人工压缩Navier-Stokes方程解的适定性[J]. 吉首大学学报（自然科学版）, 2022, 43(2): 11-16.

ZHANG Fang. Well-Posedness of Solutions of Artificially Compressed Navier Stokes Equations with Jump Noise[J]. Journal of Jishou University(Natural Sciences Edition), 2022, 43(2): 11-16.

参考文献

[1] KWEON JAE RYONG.A Posteriori Error Estimates for a Compressible Stokes System[J].NumericalMethods for Partial Differential Equations,2004,20(3):412-431.
[2] CHORIN ALEXANDRE JOEL.Numerical Solution of the Navier-Stokes equations[J].Computational Fluid Mechanics,1968,22(104):745-762.
[3] TMAM ROGER.Sur l'approximation de la Solution Des éQuations de Navier-Stokes Par la Méthode des pas Fractionnaires (II)[J].Archive for Rational Mechanics & Analysis,1969,33(5):377-385.
[4] UTPAL MANNA,JOSE-LUIS MENALDI,SRITHARAN SIVAGURU S.Stochastic 2-D Navier-Stokes Equation with Artificial Compressibility[J].Brain Research,2008,72(2):360-365.
[5] DONG Zhao,XIE Yinchao.Global Solutions of Stochastic 2D Navier-Stokes Equations with Lévy Noise[J].Science in China Series A:Mathematics,2009,52(7):1497-1524.
[6] NITHIARASU PERUMAL.An Efficient Artificial Compressibility (AC) Scheme Based on the Characteristic Based Split (CBS) Method for Incompressible Flows[J].International Journal for Numerical Methods in Engineering,2003,56(13):1815-1845.
[7] SERGIO ALBEVERIO,ZDZISAW BRZEZ〖DD(-1〗＇〖DD)〗NIAK,WU Jianglun.Existence of Global Solutions and Invariant Measures for Stochastic Differential Equations Driven By Poisson Type Noise with Non-Lipschitz Coefficients[J].Journal of Mathematical Analysis and Applications,2010,371(1):309-322.
[8] BRZEZNIAK ZDZISLAW,HAUSENBLAS ERIKA,ZHU Jiahui.2D stochastic Navier-Stokes Equations Driven by Jump Noise[J].Nonlinear Analysis:Theory,Methods & Applications,2013,79:122-139.
[9] BARBUVIOREL,SRITHARAN SIVAGURU.M-Accretive Quantization of the Vorticity Equation[M].Basel:Birkhuser,2000:296-303.
[10] BARBU VIOREL,SRITHARAN SIVAGURU S.Flow Invariance Preserving Feedback Controllers for the Navier-Stokes Equation[J].Journal of Mathematical Analysis & Applications,2001,255(1):281-307.
[11] MOHAN MANIL T,SRITHARAN SIVAGURU.New Methods for Local Solvability of Quasilinear Symmetric Hyperbolic Systems[J].Evolution Equations & Control Theory,2016,5(2):273-302.
[12] SRITHARANSIVAGURU S,SUNDAR PADMA.Large Deviations for the Two-Dimensional Navier-Stokes Equations with Multiplicative Noise[J].Stochastic Processes and their Applications,2006,116(11):1636-1659.

跳噪声扰动下人工压缩Navier-Stokes方程解的适定性

Well-Posedness of Solutions of Artificially Compressed Navier Stokes Equations with Jump Noise

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 2

编辑推荐

Metrics

本文评价

[1]	胡华书, 古传运. 一类n阶m点边值问题正解的存在唯一性[J]. 吉首大学学报（自然科学版）, 2024, 45(1): 1-6.
[2]	闻国椿. 二阶退化椭圆型方程的间断混合边值问题[J]. journal6, 2005, 26(4): 1-7.