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Convergence towards self-similar asymptotic behavior for the dissipative quasi-geostrophic equations. (English) Zbl 1121.35109

Biler, Piotr (ed.) et al., Self-similar solutions of nonlinear PDE. Selected papers of the conference, Bȩdlewo, Poland, September 5–9, 2005. Warsaw: Polish Academy of Sciences, Institute of Mathematics. Banach Center Publications 74, 95-115 (2006).
The authors study the asymptotic behavior of the solutions to the two dimensional dissipative quasigeostrophic (2DQG) equations, derived from the general case in the hypotheses of constant potential vorticity and buoyancy frequency. Global existence and uniqueness results, as well as \(L^p\) estimates on the solutions and their derivatives are obtained. It is also shown that a particular self similar solution of 2DGQ equations plays the same role as the Oseen vortex for the two-dimensional Navier-Stokes equations in the vorticity-velocity formulation.
For the entire collection see [Zbl 1104.35004].

MSC:

35Q35 PDEs in connection with fluid mechanics
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
35B40 Asymptotic behavior of solutions to PDEs
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