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Communications in Mathematical Physics

, Volume 267, Issue 1, pp 141–157 | Cite as

Dissipative Quasi-Geostrophic Equation for Large Initial Data in the Critical Sobolev Space

  • Hideyuki MiuraEmail author
Article

Abstract

The critical and super-critical dissipative quasi-geostrophic equations are investigated in \(\mathbb{R}^2\). We prove local existence of a unique regular solution for arbitrary initial data in H 2-2α which corresponds to the scaling invariant space of the equation. We also consider the behavior of the solution near t = 0 in the Sobolev space.

Keywords

Sobolev Space Local Existence Invariant Space Cancellation Property Large Initial Data 
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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Mathematical InstituteTohoku UniversitySendaiJapan

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