Communications in Mathematical Physics

, Volume 249, Issue 3, pp 511–528

A Maximum Principle Applied to Quasi-Geostrophic Equations

Authors

  • Antonio Córdoba
    • Departamento de MatemáticasUniversidad Autónoma de Madrid
  • Diego Córdoba
    • Instituto de Matemáticas y Física FundamentalConsejo Superior de Investigaciones Científicas
Article

DOI: 10.1007/s00220-004-1055-1

Cite this article as:
Córdoba, A. & Córdoba, D. Commun. Math. Phys. (2004) 249: 511. doi:10.1007/s00220-004-1055-1

Abstract

We study the initial value problem for dissipative 2D Quasi-geostrophic equations proving local existence, global results for small initial data in the super-critical case, decay of Lp-norms and asymptotic behavior of viscosity solution in the critical case. Our proofs are based on a maximum principle valid for more general flows.

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© Springer-Verlag Berlin Heidelberg 2004