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Non-radial self-similar solutions for the critical dissipative quasi-geostrophic equation. (Solutions auto-similaires non radiales pour l’équation quasi-géostrophique dissipative critique.) (French) Zbl 1155.76320
Summary: We prove the existence of self-similar solutions for the critical dissipative quasi-geostrophic equation by using the formalism of mild solutions in a space close to \(L^\infty\).

MSC:
76D05 Navier-Stokes equations for incompressible viscous fluids
26A33 Fractional derivatives and integrals
35Q35 PDEs in connection with fluid mechanics
35R10 Partial functional-differential equations
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
76U05 General theory of rotating fluids
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