Asymptotic Study of the 2D-DQGE Solutions

Journal Article
Ameur, Mongi Blel and Jamel Ben . 2014
نوع عمل المنشور: 
المجلة \ الصحيفة: 
Hindawi Publishing Corporation Journal of Function Spaces
رقم الإصدار السنوي: 
Article ID 538374,
مستخلص المنشور: 

We study the regularity of the solutions of the surface quasi-geostrophic equation with subcritical exponent 1/2 < α ≤ 1. We prove that if the initial data is small enough in the critical space Ḣ_{ 2−2α} (R^2 ), then the regularity of the solution is of exponential growth
type with respect to time and its Ḣ_{ 2−2α }(R^2 ) norm decays exponentially fast. It becomes then infinitely differentiable with respect to time and has value in all homogeneous Sobolev spaces Ḣ_s (R^2 ) for s ≥ 2 − 2α. Moreover, we give some general properties of the
global solutions.


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