旋转浅水和欧拉方程的渐近极限
2023-06-21 03:59:50刘梦雨杨建伟
四川师范大学学报（自然科学版） 2023年5期
刘梦雨 杨建伟
摘要：基于测度值解的概念，研究了旋转浅水和欧拉方程的渐近极限问题.在好初值条件下，证明了当弗劳德数趋近于零时，旋转浅水和欧拉方程的测度值解收敛于旋转湖方程的经典解.
关键词：旋转浅水和歐拉方程; 测度值解; 渐近极限
中图分类号：O175.2 文献标志码：A 文章编号：1001-8395（2023）05-0623-05
1预备知识
2引理和主要结果
3主要结论的证明
参考文献
[1] WU K C. Low Froud number limit of the rotating shallow water and Euler equation[J]. Proc Amer Math Soc，2014，142（3）：939-947.
[2] LEVERMORE C D， OLIVER M， TITI E S. Global well-posedness for models of shallow water in a basin with a varying bottom[J]. Indiana Univ Math，1996，45（2）：479-510.
[3] CHENG P， YANG J W， DAN B. Rate of convergence from the rotating Euler and shallow water equation to the rotating lake equations[J]. Bound Value Problem，2017，2017：1-9.
[4] PERNA D R J. Measure-valued solutions to conservation laws[J]. Arch Ration Mech Anal，1985，88（3）：223-270.
[5] GWIAZDA P， SWIERCZEWSKA-GWIAZDA A， WIEDEMANN E. Weak-strong uniqueness for measure-valued solutions of some compressible fluid models[J]. Nonlinearity，2015，28（11）：3873-3890.
[6] FEIREISL E， GWIAZDA P， SWIERCZEWSKA-GWIAZDA A， et al. Dissipative measure-valued solutions to the compressible Navier-Stokes system[J]. Calc Var Part Diff，2016，55（6）：141-160.
[7] BREZINA J， FEIREISL E. Measure-valued solutions to the complete Euler system[J]. J Math Soc Japan，2018，69：1227-1245.
[8] FEIREISL E， KLINGENBERG C， MARKFELDER S. On the low Mach number limit for the compressible Euler system[J]. SIAM J Math Anal，2019，51（2）：1496-1513.
[9] BREZINA J， FEIREISL E， NOVOTNY A. Stability of strong solutions to the Navier-Stokes-Fourier system[J]. SIAM J Math Anal，2020，52（2）：1761-1785.
[10] HUANG B K. On the existence of dissipative measure-valued solutions to the compressible micropolar system[J]. J Math Fluid Mech，2020，22（59）：1-16.
Asymptotic Limit of the Rotating Shallow Water and Euler EquationsLIU Mengyu，YANG Jianwei（School of Mathematics and Statistics， North China University of Water Resources and Electric Power， Zhengzhou 450046， Henan）
Abstract：In this paper， we study the asymptotic limit of the rotating shallow water and Euler equations based on the concept of measure-valued solutions. In the case of well-prepared initial data， we prove that the measure-valued solutions of the rotating shallow water and Euler equations converge to the classical solution of the rotating lake equations when the Froued number tends to zero.
Keywords：rotating shallow water and Euler equations; measure-valued solutions; asymptotic limit
2020 MSC：35B40; 35D30
（编辑周俊）
