@article{6256bd6dc45340acb2670f3156557267,
title = "Global flows with invariant measures for the inviscid modified SQG equations",
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 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. ",
keywords = "Gibbs measure, Global solutions, Invariant measure, SQG",
author = "Nahmod, {Andrea R.} and Nata{\v s}a Pavlovi{\'c} and Gigliola Staffilani and Nathan Totz",
note = "Funding Information: Andrea R. Nahmod is funded in part by NSF DMS-1201443 and DMS-1463714. Nata{\v s}a Pavlovi{\'c} is funded in part by NSF DMS-1516228. Gigliola Staffilani is funded in part by NSF DMS-1362509 and DMS-1462401. Nathan Totz is funded in part by NSF DMS-1612931. Funding Information: The authors express their gratitude to MSRI for the kind hospitality and stimulating environment during the Fall 2015 semester, where the project started while all four authors were in residence for their special jumbo program New Challenges in PDE: Deterministic Dynamics and Randomness in High and Infinite Dimensional Systems. The authors also thank IHES for their kind hospitality in Summer 2016 during of their Ondes Non Lin{\'e}aires program. Special thanks go also to Alessio Figalli, Martin Hairer, Luc Rey-Bellet, and Vlad Vicol for insightful and helpful discussions. Also we are thankful to the referee for careful reading of the manuscript and helpful suggestions for improvements.",
year = "2018",
month = jun,
day = "1",
doi = "10.1007/s40072-017-0106-5",
language = "English (US)",
volume = "6",
pages = "184--210",
journal = "Stochastics and Partial Differential Equations: Analysis and Computations",
issn = "2194-0401",
publisher = "Springer New York",
number = "2",
}