旋轉淺水和歐拉方程的漸近極限

劉夢雨　楊建偉

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

關鍵詞：旋轉淺水和歐拉方程; 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預備知識

2引理和主要結果

3主要結論的證明

參考文獻

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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

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