On an Euler-Schrödinger system appearing in laser-plasma interaction
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916749909164032 |
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| author | Bhandari, Kuntal Ducomet, Bernard Nečasová, Šarka Simon, John Sebastian H. |
| author_facet | Bhandari, Kuntal Ducomet, Bernard Nečasová, Šarka Simon, John Sebastian H. |
| contents | 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 $u_0$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_15815 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On an Euler-Schrödinger system appearing in laser-plasma interaction Bhandari, Kuntal Ducomet, Bernard Nečasová, Šarka Simon, John Sebastian H. Analysis of PDEs 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 $u_0$ 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. |
| title | On an Euler-Schrödinger system appearing in laser-plasma interaction |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2505.15815 |