Global flows with invariant measures for the inviscid modified SQG equations

Andrea R. Nahmod; Nataša Pavlović; Gigliola Staffilani; Nathan Totz

doi:10.1007/s40072-017-0106-5

Global flows with invariant measures for the inviscid modified SQG equations

Andrea R. Nahmod, Nataša Pavlović, Gigliola Staffilani, Nathan Totz

Mathematics

Research output: Contribution to journal › Article

5 Scopus citations

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.

Original language	English (US)
Pages (from-to)	184-210
Number of pages	27
Journal	Stochastics and Partial Differential Equations: Analysis and Computations
Volume	6
Issue number	2
DOIs	https://doi.org/10.1007/s40072-017-0106-5
State	Published - Jun 1 2018

Keywords

Gibbs measure
Global solutions
Invariant measure
SQG

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation
Applied Mathematics

Access to Document

10.1007/s40072-017-0106-5

Fingerprint Dive into the research topics of 'Global flows with invariant measures for the inviscid modified SQG equations'. Together they form a unique fingerprint.

Cite this

Nahmod, A. R., Pavlović, N., Staffilani, G., & Totz, N. (2018). Global flows with invariant measures for the inviscid modified SQG equations. Stochastics and Partial Differential Equations: Analysis and Computations, 6(2), 184-210. https://doi.org/10.1007/s40072-017-0106-5

@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",

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",

}

TY - JOUR

T1 - Global flows with invariant measures for the inviscid modified SQG equations

AU - Nahmod, Andrea R.

AU - Pavlović, Nataša

AU - Staffilani, Gigliola

AU - Totz, Nathan

PY - 2018/6/1

Y1 - 2018/6/1

N2 - 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.

AB - 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.

KW - Gibbs measure

KW - Global solutions

KW - Invariant measure

KW - SQG

UR - http://www.scopus.com/inward/record.url?scp=85057147748&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85057147748&partnerID=8YFLogxK

U2 - 10.1007/s40072-017-0106-5

DO - 10.1007/s40072-017-0106-5

M3 - Article

AN - SCOPUS:85057147748

VL - 6

SP - 184

EP - 210

JO - Stochastics and Partial Differential Equations: Analysis and Computations

JF - Stochastics and Partial Differential Equations: Analysis and Computations

SN - 2194-0401

IS - 2

ER -