Global Wellposedness for a Modified Critical Dissipative Quasi-Geostropic Equation
نویسنده
چکیده
In this paper we study the following modified quasi-geostrophic equation ∂tθ + u · ∇θ + ν|D| θ = 0, u = |D|Rθ with ν > 0 and 0 < α < 1. This equation was firstly introduced by Constantin-Iyer-Wu in [10]. Here, we first prove the local existence result of smooth solutions by using the energy method and the regularization effect of the transport equation with fractional diffusion, and then through constructing a suitable modulus of continuity we rule out all the possible blowup scenarios to obtain the global well-posedness of this system. Mathematics Subject Classification (2000): 76U05, 76B03, 35Q35
منابع مشابه
Global Wellposedness for a Modified Critical Dissipative Quasi-Geostrophic Equation
In this paper we study the following modified quasi-geostrophic equation ∂tθ + u · ∇θ + ν|D| θ = 0, u = |D|Rθ with ν > 0 and 0 < α < 1. This equation was firstly introduced by Constantin-Iyer-Wu in [10]. Here, we firstly prove the local existence result of smooth solutions by using the classical method, and then through constructing a suitable modulus of continuity we rule out all the possible ...
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