On the periodic Schrödinger-Debye equation
On the periodic Schrödinger-Debye equation
We study local and global well-posedness of the initial value problem for the Schrödinger-Debye equation in the <em>periodic case</em>. More precisely, we prove local well-posedness for the periodic Schrödinger-Debye equation with subcritical nonlinearity in arbitrary dimensions. Moreover, we derive a new <em>a priori</em> estimate for the $H^1$ norm of solutions …