Some new well-posedness results for the Klein-Gordon-Schrödinger system. (English) Zbl 1249.35309

Pecher, Hartmut

Differ. Integral Equ. 25, No. 1-2, 117-142 (2012).

The paper deals with the Cauchy problem for the Klein-Gordon-Schrödinger system with Yukawa coupling \(i\partial _tu+\Delta u=nu\), \(\partial _t^2n+(1-\Delta )n=| u| ^2\) in \((0,T)\times \mathbb {R}^d\), where \(d=2\) or \(d=3\). Under some assumptions on \(s\) and \(\sigma \) the local well-posedness or the global well-posedness of the problem for the initial data \(u_0\in H^s\) and \((n_0,n_1)\in H^{\sigma }\times H^{\sigma -1}\) are proved.

Reviewer: Marie Kopáčková (Praha)

MSC:

35Q55	NLS equations (nonlinear Schrödinger equations)
35L76	Higher-order semilinear hyperbolic equations

Keywords:

Klein-Gordon-Schrödinger system; well-posedness; Cauchy problem; Yukawa coupling