旋轉(zhuǎn)淺水和歐拉方程的漸近極限

劉夢(mèng)雨　楊建偉

摘要：基于測(cè)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(wèn)題.在好初值條件下，證明了當(dāng)弗勞德數(shù)趨近于零時(shí)，旋轉(zhuǎn)淺水和歐拉方程的測(cè)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(cè)度值解; 漸近極限

中圖分類號(hào)：O175.2 文獻(xiàn)標(biāo)志碼：A 文章編號(hào)：1001-8395（2023）05-0623-05

1預(yù)備知識(shí)

2引理和主要結(jié)果

3主要結(jié)論的證明

參考文獻(xiàn)

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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

（編輯周俊）