Asymptotic Study of the 2D-DQGE Solutions. (7th July 2014) - Benameur, Jamel; Blel, Mongi
Abstract : We study the regularity of the solutions of the surface quasi-geostrophic equation with subcritical exponent1 / 2 < α ≤ 1 . We prove that if the initial data is small enough in the critical spaceH ˙ 2 - 2 α ( R 2 ), then the regularity of the solution is of exponential growth type with respect to time and itsH ˙ 2 - 2 α ( R 2 ) norm decays exponentially fast. It becomes then infinitely differentiable with respect to time and has value in all homogeneous Sobolev spacesH ˙ s ( R 2 ) fors ≥ 2 - 2 α . Moreover, we give some general properties of the global solutions.