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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Hyperbolic Differential Equations

ISSN

0219-8916

e-ISSN

1793-6993

Svazek periodika

22

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

SG - Singapurská republika

Počet stran výsledku

19

Strana od-do

761-779

Kód UT WoS článku

001653940700001

EID výsledku v databázi Scopus

2-s2.0-105026805541