×

Well-posedness of the initial-boundary value problem for the Schrödinger-Boussinesq system. (English) Zbl 1474.35071

In the paper under review the Authors establish the local well-posedness of the Schrödinger-Boussinesq system on the half line with data of low regularity. The proof is based on the explicit solution formula of the linear boundary problem and the restricted norm method. Besides, it has been proved that the nonlinearity is smoother than the initial data. The results match the known results on the full line in reference [L. G. Farah, Differ. Integral Equ. 21, No. 7–8, 743–770 (2008; Zbl 1224.35027)].

MSC:

35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
35Q55 NLS equations (nonlinear Schrödinger equations)

Citations:

Zbl 1224.35027