球面上浅水方程的奇异极限
Singular Limits of the Shallow Water Equations on the Sphere
AI总结：
研究球面上浅水方程的奇异极限，证明弗劳德数与罗斯比数之比有界时解一致有界，在参数比固定且趋于零的奇异极限下，有精心准备初始数据的解趋于极限方程相应解，还得到三尺度奇异极限的收敛结果。
AI中文摘要：
研究表明，在快速旋转球体上，当弗劳德数与罗斯比数之比有界时，微可压缩浅水方程的解是一致有界的。此外，在这些参数之比保持固定且都趋于零时的奇异极限情况下，具有精心准备的初始数据的解趋于极限方程的相应解。对于弗劳德数比罗斯比数更快趋于零的三尺度奇异极限，也得到了一个收敛结果。
英文摘要：
Solutions of the slightly compressible shallow water equations on a rapidly rotating sphere are shown to be bounded uniformly when ratio of the Froude number to the Rossby number is bounded. Moreover, in the singular limit in which the ratio of those parameters remains fixed while they both tend to zero, solutions with well-prepared initial data tend to corresponding solutions of limit equations. A convergence result is also obtained for the three-scale singular limit in which the Froude number tends to zero faster than the Rossby number.
