منابع مشابه
On the critical dissipative quasi-geostrophic equation
The 2D quasi-geostrophic (QG) equation is a two dimensional model of the 3D incompressible Euler equations. When dissipation is included in the model then solutions always exist if the dissipation’s wave number dependence is super-linear. Below this critical power the dissipation appears to be insufficient. For instance, it is not known if the critical dissipative QG equation has global smooth ...
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The 2D quasi-geostrophic equation t + u · ∇ + (− ) = 0, u=R⊥( ) is a two-dimensional model of the 3D hydrodynamics equations. When 1 2 , the issue of existence and uniqueness concerning this equation becomes difficult. It is shown here that this equation with either = 0 or > 0 and 0 1 2 has a unique local in time solution corresponding to any initial datum in the space Cr ∩ Lq for r > 1 and q >...
متن کاملEventual regularization for the slightly supercritical quasi-geostrophic equation
We prove that weak solutions of a slightly supercritical quasi-geostrophic equation become smooth for large time. We prove it using a De Giorgi type argument using ideas from a recent paper by Caffarelli and Vasseur.
متن کاملAlmost sharp fronts for the surface quasi-geostrophic equation.
We investigate the evolution of "almost sharp" fronts for the surface quasi-geostrophic equation. This equation was originally introduced in the geophysical context to investigate the formation and evolution of fronts, i.e., discontinuities between masses of hot and cold air. These almost sharp fronts are weak solutions of quasi-geostrophic with large gradient. We relate their evolution to the ...
متن کاملNumerical Simulations of a 2d Quasi Geostrophic Equation
This paper deals with the numerical simulations of the 2D generalized quasi geostrophic equation, where the velocity field is related to the solution θ by a rotation of Riesz transforms. Depending on the parameters of the problem, we present numerical evidences for long time behavior of the solution such as global existence effects or blow up in finite time.
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2015
ISSN: 0022-0396
DOI: 10.1016/j.jde.2015.02.022