On an Euler-Schrödinger system appearing in laser-plasma interaction

2025/05/21 by Kuntal Bhandari, Bhandari, Kuntal, Bernard Ducomet +5
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2505.15815

openalex publication_date 2025/05/21 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28

Abstract

We consider the Cauchy problem for the barotropic Euler system coupled to a vector Schrödinger equation in the whole space. Assuming that the initial density and vector potential are small enough, and that the initial velocity is close to some reference vector field u₀ such that the spectrum of Du₀ is bounded away from zero, we prove the existence of a global-in-time unique solution with (fractional) Sobolev regularity. Moreover, we obtain some algebraic time decay estimates of the solution. Our work extends the papers by D. Serre and M. Grassin [11, 13, 19] and previous works by B. Ducomet and co-authors [4, 8] dedicated to the compressible Euler-Poisson system.

Citations

• Global solutions of Euler-Maxwell equations with dissipation
• The global existence issue for the compressible Euler system with Poisson or Helmholtz couplings
• A short proof of commutator estimates
• Local existence of solutions to the Euler-Poisson system, including densities without compact support
• The Cauchy problem for quasi-linear symmetric hyperbolic systems

Related

• The global existence issue for the compressible Euler system with Poisson or Helmholtz couplings
• Global existence for the Euler-Maxwell system
• The global Cauchy problem for the Euler-Riesz equations
• Global Existence of Solutions to the Compressible Euler Equations with Time-dependent Damping and Logarithmic State Equation
• Global existence of a radiative Euler system coupled to an electromagnetic field