Asymptotic behavior of the solutions to the 2D dissipative quasi-geostrophic flows
نویسنده
چکیده
In this paper we derive a decay rate of the L-norm of the solution to the 2-D dissipative quasi-geostrophic flows comparing with the corresponding linear equation. We use a new, concise and direct method to avoid using the Fourier splitting technique completely and make the paper be self-contained without using any previous decay result. Mathematics Subject Classification(2000): 35Q35, 76D05
منابع مشابه
A Maximum Principle Applied to Quasi-Geostrophic Equations
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 L-norms and asymptotic behavior of viscosity solution in the critical case. Our proofs are based on a maximum principle valid for more general flows.
متن کاملRegularity Criteria for the Dissipative Quasi-geostrophic Equations in Hölder Spaces
We study regularity criteria for weak solutions of the dissipative quasi-geostrophic equation (with dissipation (−∆)γ/2, 0 < γ ≤ 1). We show in this paper that if θ ∈ C((0, T ); C1−γ), or θ ∈ Lr((0, T ); Cα) with α = 1−γ+ γ r is a weak solution of the 2D quasi-geostrophic equation, then θ is a classical solution in (0, T ]× R2. This result improves our previous result in [18].
متن کاملHigher Regularity for the Critical and Super-critical Dissipative Quasi-geostrophic Equations
We study the critical and super-critical dissipative quasi-geostrophic equations in R or T. Higher regularity of mild solutions with arbitrary initial data in Ḣ is proved. As a corollary, we obtain a global existence result for the critical 2D quasigeostrophic equations with periodic Ḣ data. Some decay in time estimates are also provided.
متن کاملOn the Global Solutions of the Super-critical 2d Quasi-geostrophic Equation in Besov Spaces
In this paper we study the super-critical 2D dissipative quasi-geostrophic equation. We obtain some regularization effects allowing us to prove global well-posedness result for small initial data lying in critical Besov spaces constructed over Lebesgue spaces L, with p ∈ [1,∞]. Local results for arbitrary initial data are also given.
متن کاملGlobal Solutions of the 2D Dissipative Quasi-Geostrophic Equation in Besov Spaces
The two-dimensional (2D) quasi-geostrophic (QG) equation is a 2D model of the 3D incompressible Euler equations, and its dissipative version includes an extra term bearing the operator (−∆)α with α ∈ [0, 1]. Existing research appears to indicate the criticality of α = 1 2 in the sense that the issue of global existence for the 2D dissipative QG equation becomes extremely difficult when α ≤ 1 2 ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011