Inhaltszusammenfassung

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. ...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.» weiterlesen» einklappen

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