劉夢雨　楊建偉

摘要：基于測度值解的概念，研究了旋轉(zhuǎn)淺水和歐拉方程的漸近極限問題.在好初值條件下，證明了當弗勞德數(shù)趨近于零時，旋轉(zhuǎn)淺水和歐拉方程的測度值解收斂于旋轉(zhuǎn)湖方程的經(jīng)典解.

關(guān)鍵詞：旋轉(zhuǎn)淺水和歐拉方程; 測度值解; 漸近極限

中圖分類號：O175.2 文獻標志碼：A 文章編號：1001-8395（2023）05-0623-05

1預(yù)備知識

2引理和主要結(jié)果

3主要結(jié)論的證明

參考文獻

[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

（編輯周俊）