Critical SQG in Bounded Domains

被引：31
作者：
Constantin P. [1 ]
Ignatova M. [1 ]
机构：
[1] Department of Mathematics, Princeton University, Princeton, 08544, NJ
来源：
Annals of PDE | / 2卷 / 2期
基金：
美国国家科学基金会;
关键词：
Bounded domains; Global regularity; Nonlinear maximum principle; SQG;
D O I：
10.1007/s40818-016-0017-1
中图分类号：
学科分类号：
摘要：
We consider the critical dissipative SQG equation in bounded domains, with the square root of the Dirichlet Laplacian dissipation. We prove global a priori interior Cα and Lipschitz bounds for large data. © 2016, Springer International Publishing AG.
引用
收藏
相关论文
共 24 条
[1]  
Cabre X., Tan J., Positive solutions of nonlinear problems involving the square root of the Laplacian, Adv. Math., 224, 5, pp. 2052-2093, (2010)
[2]  
Caffarelli L.A., Vasseur A., Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation, Ann. Math., 171, 3, pp. 1903-1930, (2010)
[3]  
Castro A., Cordoba D., Gomez-Serrano J., Martin A., Remarks on geometric properties of the SQG sharp front and the alpha-patches, Discret. Contin. Dyn. Syst., 34, 12, pp. 5045-5059, (2014)
[4]  
Global smooth solutions for the inviscid SQG equation, Preprint (2016). Arxiv, (1603)
[5]  
Constantin P., Geometric statistics in turbulence, SIAM Rev., 36, 1, pp. 73-98, (1994)
[6]  
Constantin P., Ignatova M., Remarks on the fractional Laplacian with Dirichlet boundary conditions and applications, Int. Math. Res. Not., (2016)
[7]  
Constantin P., Vicol V., Nonlinear maximum principles for dissipative linear nonlocal operators and applications, GAFA, 22, pp. 1289-1321, (2012)
[8]  
Constantin P., Wu J., Regularity of Hölder continuous solutions of the supercritical quasi-geostrophic equation, Ann. Inst. H. Poincaré Anal. Non Linéaire, 25, 6, pp. 1103-1110, (2008)
[9]  
Constantin P., Majda A.J., Tabak E., Formation of strong fronts in the 2 -D quasigeostrophic thermal active scalar, Nonlinearity, 7, 6, pp. 1495-1533, (1994)
[10]  
Constantin P., Cordoba D., Wu J., On the critical dissipative quasi-geostrophic equation, Indiana Univ. Math. J., 50, Special, pp. 97-107, (2001)
123