Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí sinh học đề tài :Global existence for the regularized surface Quasi-geostrophic equation and its inviscid limits | Li and Wang Boundary Value Problems 2011 2011 41 http content 2011 1 41 o Boundary Value Problems a SpringerOpen Journal RESEARCH Open Access Global existence for the regularized surface Quasi-geostrophic equation and its inviscid limits Linrui Li and Shu Wang 1 Correspondence linrui020213@ College of Applied Sciences Beijing University of Technology Ping Le Yuan 100 Chaoyang District Beijing 100124 People s Republic of China Springer Abstract We study solutions of the initial value problem for the 2D regularized surface quasi-geostrophic RSQG equation. For H1 Q n Lq Q q 2 to initial data we prove the global existence and uniqueness of weak solution for RSQG equation with subcritical powers. For RSQG equation we establish some regularization results and prove the inviscid limit of the RSQG equation to the classical quasi-geostrophic equation. Mathematics Subject Classifications 35Q35 76U05 86A10. Keywords regularized surface quasi-geostrophic equation initial value problem existence uniqueness regularization 1 Introduction The quasi-geostrophic equation QG with periodic boundary conditions on a basic period box w 0 2n 2 c R2 is 0t div u0 0 1 -A 2 p 0 vxp u ị 0dx 0 y pdx 0 ị udx 0 0 x 0 00 x . where 0 x t is a real-valued function of x and t which represents the potential temperature and u represents the incompressible horizontal velocity at the surface. The advective velocity u in these equations is determined from 0 by a stream function Ộ via the auxiliary relations dp dp u U1 U2 1 - - d x2 d x1 and the relationship 2. The equality relating u to 0 in and 2 can be reformulated in terms of periodic Riesz transforms u -dx2 A-10 dxi A-10 -R20 R10 2011 Li and Wang licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License http licenses by which permits unrestricted use distribution and reproduction in any medium provided the .
