Asymptotic Study of the 2D-DQGE Solutions

Journal Article

Ameur, Mongi Blel and Jamel Ben . 2014

• نوع عمل المنشور: theoric
• رابط المنشور على الويب: http://dx.doi.org/10.1155/2014/538374
• المجلة \ الصحيفة: Hindawi Publishing Corporation Journal of Function Spaces
• رقم الإصدار السنوي: Article ID 538374,
• الصفحات: 1-6

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.