arXiv subjects

Catalina Jurja

Publications and source records attributed to Catalina Jurja.

3 recordsLinked to original sources

arXiv2026

Global dynamics in the 3D pressureless Euler-Poisson system for ions

In this work we consider the pressureless Euler-Poisson system on $\mathbb{R}^3$ describing ion dynamics, which is a common model in the study of cold plasma. We prove global regularity and scattering for small, irrotational velocity fields around a constant density profile. At the heart of the result is a dispersive mechanism leading to amplitude decay at the full rate in $3$D. This fast decay feature and a favourable structure of the nonlinearity allow to control quadratic interactions globally.

math.AP↗

arXiv2026

Long-time stability of a stably stratified rest state in the inviscid 2D Boussinesq equation

We establish the nonlinear stability on a timescale $O(\varepsilon^{-2})$ of a linearly, stably stratified rest state in the inviscid Boussinesq system on $\mathbb{R}^2$. Here $\varepsilon>0$ denotes the size of an initially sufficiently small, Sobolev regular and localized perturbation. A similar statement also holds for the related dispersive SQG equation. At the core of this result is a dispersive effect due to anisotropic internal gravity waves. At the linearized level, this gives rise to amplitude decay at a rate of $t^{-1/2}$, as observed in [EW15]. We establish a refined version of this, and propagate nonlinear control via a detailed analysis of nonlinear interactions using the method of partial symmetries developed in [GPW23].

math.AP↗

arXiv2025

The effect of linear stratification on the stability of a rest state in the 2D inviscid Boussinesq system

We investigate and quantify the effect of stratification on the stability time of a stably stratified rest state for the 2D inviscid Boussinesq system on $\mathbb{R}^2$. As an important consequence, we obtain stability of the steady state starting from an $\varepsilon$-sized initial perturbation of Sobolev regularity $H^{3^+}$ on a timescale $\mathcal{O}(\varepsilon^{-4/3})$. In our setting, stratification induces dispersion and at the core of our approach are inhomogeneous Strichartz estimates used to control nonlinear contributions. This allows to keep only $L^2-$based regularity assumptions on the initial perturbation, whereas previous works impose additional localizations to achieve this timescale. We prove the analogous result for the related dispersive SQG equation.

math.AP↗