The Semigeostrophic-Euler Limit: Lifespan Lower Bounds and $O(\varepsilon)$ Velocity Stability
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915866437746688 |
|---|---|
| author | Armegioiu, Victor |
| author_facet | Armegioiu, Victor |
| contents | We study the two-dimensional semigeostrophic system on the flat torus in the small-amplitude scaling and quantify its approximation by incompressible Euler in dual variables. On a natural perturbative bootstrap window for the Monge--Ampère coupling, we prove two strong stability results: an $O(\eps)$ estimate for the velocity in $L^2$, and an $O(\eps)$ estimate in Wasserstein distance for the associated physical densities. The latter is deduced from a more general comparison theorem, independent of the bootstrap regime, which combines the deterministic flow representation for the smooth Euler solution with a superposition representation for the semigeostrophic continuity equation. We also prove a lifespan lower bound with a logarithmic improvement over the standard hyperbolic scale, namely $T_*(\eps)\gtrsim \eps^{-1}\log\log(1/\eps)$ in physical time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_04797 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Semigeostrophic-Euler Limit: Lifespan Lower Bounds and $O(\varepsilon)$ Velocity Stability Armegioiu, Victor Analysis of PDEs Fluid Dynamics We study the two-dimensional semigeostrophic system on the flat torus in the small-amplitude scaling and quantify its approximation by incompressible Euler in dual variables. On a natural perturbative bootstrap window for the Monge--Ampère coupling, we prove two strong stability results: an $O(\eps)$ estimate for the velocity in $L^2$, and an $O(\eps)$ estimate in Wasserstein distance for the associated physical densities. The latter is deduced from a more general comparison theorem, independent of the bootstrap regime, which combines the deterministic flow representation for the smooth Euler solution with a superposition representation for the semigeostrophic continuity equation. We also prove a lifespan lower bound with a logarithmic improvement over the standard hyperbolic scale, namely $T_*(\eps)\gtrsim \eps^{-1}\log\log(1/\eps)$ in physical time. |
| title | The Semigeostrophic-Euler Limit: Lifespan Lower Bounds and $O(\varepsilon)$ Velocity Stability |
| topic | Analysis of PDEs Fluid Dynamics |
| url | https://arxiv.org/abs/2601.04797 |