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 | |
| State | Published - Jan 1 2019 |
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All Science Journal Classification (ASJC) codes
- Analysis
- Computational Mathematics
- Applied Mathematics
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The inviscid limit of navier-stokes equations for vortex-wave data on R2. / Nguyen, Toan; Nguyen, Trinh T.
In: SIAM Journal on Mathematical Analysis, Vol. 51, No. 3, 01.01.2019, p. 2575-2598.Research output: Contribution to journal › Article
TY - JOUR
T1 - The inviscid limit of navier-stokes equations for vortex-wave data on R2
AU - Nguyen, Toan
AU - Nguyen, Trinh T.
PY - 2019/1/1
Y1 - 2019/1/1
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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U2 - 10.1137/19M1246602
DO - 10.1137/19M1246602
M3 - Article
VL - 51
SP - 2575
EP - 2598
JO - SIAM Journal on Mathematical Analysis
JF - SIAM Journal on Mathematical Analysis
SN - 0036-1410
IS - 3
ER -