Global flows with invariant measures for the inviscid modified SQG equations
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Author(s)
Nahmod, Andrea R
Pavlović, Nataša
Totz, Nathan
Staffilani, Gigliola
Date Issued
October 2017
Journal
Stochastics and Partial Differential Equations: Analysis and Computations
Publisher
Springer US
Citation
Nahmod, Andrea R., et al. “Global Flows with Invariant Measures for the Inviscid Modified SQG Equations.” Stochastics and Partial Differential Equations: Analysis and Computations, vol. 6, no. 2, June 2018, pp. 184–210.
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Author's final manuscript
Abstract
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 L[superscript 2]-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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1007/s40072-017-0106-5
