Abstract
This paper studies the pressureless Euler-Poisson system and its fully nonlinear counterpart, the Euler-Monge-Ampère system, where the fully nonlinear Monge-Ampère equation substitutes for the linear Poisson equation. While the first is a model of plasma physics, the second is derived as a geometric approximation to the Euler incompressible equations. Using energy estimates, convergence of both systems to the Euler incompressible equations is proved.
| Original language | English |
|---|---|
| Pages (from-to) | 1141-1167 |
| Number of pages | 27 |
| Journal | Communications in Partial Differential Equations |
| Volume | 30 |
| Issue number | 7-9 |
| DOIs | |
| Publication status | Published - 2005 |
| Externally published | Yes |
Keywords
- Incompressible Euler equations
- Optimal transportation
- Quasineutral limit
Cite this
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Quasi-neutral limit of the Euler-Poisson and Euler-Monge-Ampère systems. / Loeper, Grégoire.
In: Communications in Partial Differential Equations, Vol. 30, No. 7-9, 2005, p. 1141-1167.Research output: Contribution to journal › Article › Research › peer-review
TY - JOUR
T1 - Quasi-neutral limit of the Euler-Poisson and Euler-Monge-Ampère systems
AU - Loeper, Grégoire
PY - 2005
Y1 - 2005
N2 - This paper studies the pressureless Euler-Poisson system and its fully nonlinear counterpart, the Euler-Monge-Ampère system, where the fully nonlinear Monge-Ampère equation substitutes for the linear Poisson equation. While the first is a model of plasma physics, the second is derived as a geometric approximation to the Euler incompressible equations. Using energy estimates, convergence of both systems to the Euler incompressible equations is proved.
AB - This paper studies the pressureless Euler-Poisson system and its fully nonlinear counterpart, the Euler-Monge-Ampère system, where the fully nonlinear Monge-Ampère equation substitutes for the linear Poisson equation. While the first is a model of plasma physics, the second is derived as a geometric approximation to the Euler incompressible equations. Using energy estimates, convergence of both systems to the Euler incompressible equations is proved.
KW - Incompressible Euler equations
KW - Optimal transportation
KW - Quasineutral limit
UR - http://www.scopus.com/inward/record.url?scp=27744590550&partnerID=8YFLogxK
U2 - 10.1080/03605300500257545
DO - 10.1080/03605300500257545
M3 - Article
VL - 30
SP - 1141
EP - 1167
JO - Communications in Partial Differential Equations
JF - Communications in Partial Differential Equations
SN - 0360-5302
IS - 7-9
ER -