Weak solutions for the derivative nonlinear Schrödinger equation

RIAL, D. F.

JOURNAL OF NONLINEAR ANALYSIS

Año: 2002 vol. 49 p. 149 - 158

0362-546X

We study the initial value problem for the derivative nonlinear Schroedinger equation. We show the existence of global in time $L^2$-weak solutions as well as smoothing effect for the equation. To prove the theorem we use similar arguments as[T. Kato, Adv. Math., Suppl. Stud., 8, 93-128 (1983; Zbl 0549.34001)] for the Korteweg-de Vries equation. We introduce an artificial viscosity term to obtain a weak solution of the previous problem.