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Open Access Research

Global existence for the regularized surface Quasi-geostrophic equation and its inviscid limits

Linrui Li* and Shu Wang

Author affiliations

College of Applied Sciences, Beijing University of Technology, Ping Le Yuan 100, Chaoyang District, Beijing 100124, People's Republic of China

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Citation and License

Boundary Value Problems 2011, 2011:41  doi:10.1186/1687-2770-2011-41

Published: 27 October 2011

Abstract

We study solutions of the initial value problem for the 2D regularized surface quasi-geostrophic (RSQG) equation. For <a onClick="popup('http://www.boundaryvalueproblems.com/content/2011/1/41/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2011/1/41/mathml/M1">View MathML</a> initial data, we prove the global existence and uniqueness of weak solution for RSQG equation with subcritical powers. For RSQG equation, we establish some regularization results and prove the inviscid limit of the RSQG equation to the classical quasi-geostrophic equation.

Mathematics Subject Classifications

35Q35; 76U05; 86A10.

Keywords:
regularized surface quasi-geostrophic equation; initial value problem; existence; uniqueness; regularization