Global flows with invariant measures for the inviscid modified SQG equations

被引：12
作者：
Nahmod, Andrea R. [1 ]
Pavlovic, Natasa [2 ]
Staffilani, Gigliola [3 ]
Totz, Nathan [4 ]
机构：
[1] Univ Massachusetts, Dept Math, 710 N Pleasant St, Amherst, MA 01003 USA
[2] Univ Texas Austin, Dept Math, 2515 Speedway,Stop,C1200, Austin, TX 78712 USA
[3] MIT, Dept Math, 77 Massachusetts Ave, Cambridge, MA 02139 USA
[4] Univ Miami, 1365 Mem Dr, Coral Gables, FL 33146 USA
来源：
STOCHASTICS AND PARTIAL DIFFERENTIAL EQUATIONS-ANALYSIS AND COMPUTATIONS | 2018年 / 6卷 / 02期
基金：
美国国家科学基金会;
关键词：
SQG; Gibbs measure; Invariant measure; Global solutions; QUASI-GEOSTROPHIC EQUATION; DYNAMICS; SPECTRA; SPACES; EULER;
D O I：
10.1007/s40072-017-0106-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the family known as modified or generalized surface quasi-geostrophic equations (mSQG) consisting of the classical inviscid surface quasi-geostrophic (SQG) equation together with a family of regularized active scalars given by introducing a smoothing operator of nonzero but possibly arbitrarily small degree. This family naturally interpolates between the 2D Euler equation and the SQG equation. For this family of equations we construct an invariant measure on a rough L2-based Sobolev space and establish the existence of solutions of arbitrarily large lifespan for initial data in a set of full measure in the rough Sobolev space.
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页码：184 / 210
页数：27
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