Monotonicity method applied to the complex Ginzburg-Landau and related equations
global existence of unique strong solutions
A new inequality in monotonicity methods is derived. It is based on the sectorial estimates of \(-\Delta\) in \(L^{p+1}\) and the nonlinear operator \(u\mapsto|u|^{p-1}u\) appearing in the equation.NEWLINENEWLINENEWLINEBy the inequality the global existence of unique strong solutions is established for the complex Ginzburg-Landau equation. The inequality also yields the global existence of unique strong solution for nonlinear Schrödinger type equation with monotone nonlinearity.
scientific article; zbMATH DE number 1733406
scientific article