On a Euler-Schrödinger system appearing in laser-plasma interaction
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F25%3A00644183" target="_blank" >RIV/67985840:_____/25:00644183 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1142/S0219891625500213" target="_blank" >https://doi.org/10.1142/S0219891625500213</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1142/S0219891625500213" target="_blank" >10.1142/S0219891625500213</a>
Alternative languages
Result language
angličtina
Original language name
On a Euler-Schrödinger system appearing in laser-plasma interaction
Original language description
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 [Existence de solutions globales et régulières aux équations d’Euler pour un gaz parfait isentropique, C.R. Acad. Sci. Paris, Série I 325 (1997) 721–726, Global smooth solutions to Euler equations for a perfect gas, Indiana Univ. Math. J. 47 (1998) 1397–1432, Solutions classiques globales des équations d’Euler pour un fluide parfait compressible, Ann. Inst. Fourier, Grenoble 47 (1997) 139–159] and previous works by B. Ducomet and co-authors [The global existence issue for the compressible Euler system with Poisson or Helmholtz couplings, J. Hyper. Differ. Equ. 18(1) (2021) 169–193, On the the global existence for the compressible Euler-Poisson system, and the instability of static solutions, J. Evol. Equ. 21(3) (2021) 3035–3054] dedicated to the compressible Euler–Poisson system.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Hyperbolic Differential Equations
ISSN
0219-8916
e-ISSN
1793-6993
Volume of the periodical
22
Issue of the periodical within the volume
4
Country of publishing house
SG - SINGAPORE
Number of pages
19
Pages from-to
761-779
UT code for WoS article
001653940700001
EID of the result in the Scopus database
2-s2.0-105026805541