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arXiv · 2505.15815

On an Euler-Schr\"{o}dinger system appearing in laser-plasma interaction

Kuntal Bhandari·Bernard Ducomet·Šarka Nečasová·John Sebastian H. Simon
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Abstract

We consider the Cauchy problem for the barotropic Euler system coupled to a vector Schr\"{o}dinger 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 $u_0$ such that the spectrum of $Du_0$ 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.

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Kuntal Bhandari, Bernard Ducomet, Šarka Nečasová, John Sebastian H. Simon. 2025-05-21. On an Euler-Schr\"{o}dinger system appearing in laser-plasma interaction. https://arxiv.org/abs/2505.15815

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