2015/12/01 by Michele Coti Zelati, Zelati, Michele Coti
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Stability and Controllability of Differential Equations #math.AP
paper · pdf · doi:10.48550/arxiv.1512.00497
v2: 22 pages, added sections 5 and 6
openalex publication_date 2015/12/01 · arxiv created 2017/04/18 · arxiv updated 2017/04/20 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
We consider the subcritical SQG equation in its natural scale invariant Sobolev space and prove the existence of a global attractor of optimal regularity. The proof is based on a new energy estimate in Sobolev spaces to bootstrap the regularity to the optimal level, derived by means of nonlinear lower bounds on the fractional laplacian. This estimate appears to be new in the literature, and allows a sharp use of the subcritical nature of the L^∞ bounds for this problem. As a byproduct, we obtain attractors for weak solutions as well. Moreover, we study the critical limit of the attractors and prove their stability and upper-semicontinuity with respect to the strength of the diffusion.