Global solutions to the lagrangian averaged navier-stokes equation in low-regularity besov spaces

Nathan Pennington

Global solutions to the lagrangian averaged navier-stokes equation in low-regularity besov spaces

Research output: Contribution to journal › Article

Abstract

The Lagrangian Averaged Navier-Stokes (LANS) equations are a recently derived approximation to the Navier-Stokes equations. Existence of global solutions for the LANS equation has been proven for initial data in the Sobolev space H^3/4,2(R³) and in the Besov space B^n/2 _2,q (Rⁿ). In this paper, we use an interpolation-based method to prove the existence of global solutions to the LANS equation with initial data in B^3/p _p,q (R³) for any p > n.

Original language	English (US)
Pages (from-to)	697-724
Number of pages	28
Journal	Advances in Differential Equations
Volume	17
Issue number	7-8
State	Published - Dec 1 2012
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

Access to Document

Fingerprint Dive into the research topics of 'Global solutions to the lagrangian averaged navier-stokes equation in low-regularity besov spaces'. Together they form a unique fingerprint.

Cite this

Pennington, N. (2012). Global solutions to the lagrangian averaged navier-stokes equation in low-regularity besov spaces. Advances in Differential Equations, 17(7-8), 697-724.

@article{3745276ab23f47f785aa895170c186e3,

title = "Global solutions to the lagrangian averaged navier-stokes equation in low-regularity besov spaces",

abstract = "The Lagrangian Averaged Navier-Stokes (LANS) equations are a recently derived approximation to the Navier-Stokes equations. Existence of global solutions for the LANS equation has been proven for initial data in the Sobolev space H3/4,2(R3) and in the Besov space Bn/2 2,q (Rn). In this paper, we use an interpolation-based method to prove the existence of global solutions to the LANS equation with initial data in B3/p p,q (R3) for any p > n.",

author = "Nathan Pennington",

year = "2012",

month = dec,

day = "1",

language = "English (US)",

volume = "17",

pages = "697--724",

journal = "Advances in Differential Equations",

issn = "1079-9389",

publisher = "Khayyam Publishing, Inc.",

number = "7-8",

}

TY - JOUR

T1 - Global solutions to the lagrangian averaged navier-stokes equation in low-regularity besov spaces

AU - Pennington, Nathan

PY - 2012/12/1

Y1 - 2012/12/1

N2 - The Lagrangian Averaged Navier-Stokes (LANS) equations are a recently derived approximation to the Navier-Stokes equations. Existence of global solutions for the LANS equation has been proven for initial data in the Sobolev space H3/4,2(R3) and in the Besov space Bn/2 2,q (Rn). In this paper, we use an interpolation-based method to prove the existence of global solutions to the LANS equation with initial data in B3/p p,q (R3) for any p > n.

AB - The Lagrangian Averaged Navier-Stokes (LANS) equations are a recently derived approximation to the Navier-Stokes equations. Existence of global solutions for the LANS equation has been proven for initial data in the Sobolev space H3/4,2(R3) and in the Besov space Bn/2 2,q (Rn). In this paper, we use an interpolation-based method to prove the existence of global solutions to the LANS equation with initial data in B3/p p,q (R3) for any p > n.

UR - http://www.scopus.com/inward/record.url?scp=84893721791&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84893721791&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84893721791

VL - 17

SP - 697

EP - 724

JO - Advances in Differential Equations

JF - Advances in Differential Equations

SN - 1079-9389

IS - 7-8

ER -