The inviscid limit of navier-stokes equations for vortex-wave data on R2

Toan T. Nguyen; Trinh T. Nguyen

doi:10.1137/19M1246602

The inviscid limit of navier-stokes equations for vortex-wave data on R2

Toan T. Nguyen, Trinh T. Nguyen

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We establish the inviscid limit of the incompressible Navier-Stokes equations on the whole plane R2 for initial data having vorticity as a superposition of point vortices and a regular component. In particular, this rigorously justifies the vortex-wave system from the physical Navier- Stokes flows in the vanishing viscosity limit, a model that was introduced by Marchioro and Pulvirenti in the early 90s to describe the dynamics of point vortices in a regular ambient vorticity background. The proof rests on the previous analysis of Gallay in his derivation of the vortex-point system.

Original language	English (US)
Pages (from-to)	2575-2598
Number of pages	24
Journal	SIAM Journal on Mathematical Analysis
Volume	51
Issue number	3
DOIs	https://doi.org/10.1137/19M1246602
State	Published - 2019

All Science Journal Classification (ASJC) codes

Analysis
Computational Mathematics
Applied Mathematics

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10.1137/19M1246602

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title = "The inviscid limit of navier-stokes equations for vortex-wave data on R2",

abstract = "We establish the inviscid limit of the incompressible Navier-Stokes equations on the whole plane R2 for initial data having vorticity as a superposition of point vortices and a regular component. In particular, this rigorously justifies the vortex-wave system from the physical Navier- Stokes flows in the vanishing viscosity limit, a model that was introduced by Marchioro and Pulvirenti in the early 90s to describe the dynamics of point vortices in a regular ambient vorticity background. The proof rests on the previous analysis of Gallay in his derivation of the vortex-point system.",

author = "Nguyen, {Toan T.} and Nguyen, {Trinh T.}",

note = "Funding Information: \ast Received by the editors February 25, 2019; accepted for publication (in revised form) April 2, 2019; published electronically June 20, 2019. http://www.siam.org/journals/sima/51-3/M124660.html Funding: This work was supported by National Science Foundation grant DMS-1764119 and an AMS Centennial Fellowship. \dagger Department of Mathematics, Penn State University, University Park, PA 16803 (nguyen@math. psu.edu, txn5114@psu.edu).",

year = "2019",

doi = "10.1137/19M1246602",

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AU - Nguyen, Toan T.

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N1 - Funding Information: \ast Received by the editors February 25, 2019; accepted for publication (in revised form) April 2, 2019; published electronically June 20, 2019. http://www.siam.org/journals/sima/51-3/M124660.html Funding: This work was supported by National Science Foundation grant DMS-1764119 and an AMS Centennial Fellowship. \dagger Department of Mathematics, Penn State University, University Park, PA 16803 (nguyen@math. psu.edu, txn5114@psu.edu).

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N2 - We establish the inviscid limit of the incompressible Navier-Stokes equations on the whole plane R2 for initial data having vorticity as a superposition of point vortices and a regular component. In particular, this rigorously justifies the vortex-wave system from the physical Navier- Stokes flows in the vanishing viscosity limit, a model that was introduced by Marchioro and Pulvirenti in the early 90s to describe the dynamics of point vortices in a regular ambient vorticity background. The proof rests on the previous analysis of Gallay in his derivation of the vortex-point system.

AB - We establish the inviscid limit of the incompressible Navier-Stokes equations on the whole plane R2 for initial data having vorticity as a superposition of point vortices and a regular component. In particular, this rigorously justifies the vortex-wave system from the physical Navier- Stokes flows in the vanishing viscosity limit, a model that was introduced by Marchioro and Pulvirenti in the early 90s to describe the dynamics of point vortices in a regular ambient vorticity background. The proof rests on the previous analysis of Gallay in his derivation of the vortex-point system.

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