Euler equation on a rotating surface

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• 作者：Michael Taylor ^{met@math.unc.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35Q31 ; 35R09
• 刊名：Journal of Functional Analysis
• 出版年：2016
• 出版时间：15 May 2016
• 年：2016
• 卷：270
• 期：10
• 页码：3884-3945
• 全文大小：948 K

文摘

We study 2D Euler equations on a rotating surface, subject to the effect of the Coriolis force, with an emphasis on surfaces of revolution. We bring in conservation laws that yield long time estimates on solutions to the Euler equation, and examine ways in which the solutions behave like zonal fields, building on previous works that have examined how such 2D Euler equations can account for the observed band structure of rapidly rotating planets. Specific results include both an analysis of time averages of solutions and a study of stability of stationary zonal fields. The latter study includes both analytical and numerical work.