Among nonlinear PDEs, dispersive and wave equations form an important class of
equations. These include the nonlinear Schrodinger equation, the nonlinear wave equation …

This textbook introduces the well-posedness theory for initial-value problems of nonlinear,
dispersive partial differential equations, with special focus on two key models, the Korteweg …

In a recent paper, Kenig, Ponce and Vega study the low regularity behavior of the focusing
nonlinear Schrödinger (NLS), focusing modified Korteweg-de Vries (mKdV), and complex …

We prove global well-posedness of the Korteweg--de Vries equation for initial data in the
space H^-1(R). This is sharp in the class of H^s(R) spaces. Even local well-posedness was …

1. Fourier multiplier, function space [symbol]. 1.1. Schwartz space, tempered distribution,
Fourier transform. 1.2. Fourier multiplier on L [symbol]. 1.3. Dyadic decomposition, Besov …

GLOBAL WELLPOSEDNESS OF KdV IN H (T,R) Page 1 GLOBAL WELLPOSEDNESS OF
KdV IN H −1 (T,R) T. KAPPELER and P. TOPALOV Abstract By the inverse method we show …

We review recent progress on the long-time regularity of solutions of the Cauchy problem for
the water waves equations, in two and three dimensions. We begin by introducing the free …

Global existence and scattering for rough solutions of a nonlinear Schrödinger equation on
â—š³ Page 1 Global Existence and Scattering for Rough Solutions of a …

Traveling wave solutions of the Degasperis–Procesi equation Page 1 J. Math. Anal. Appl. 306
(2005) 72–82 www.elsevier.com/locate/jmaa Traveling wave solutions of the Degasperis–Procesi …

We prove an endpoint multilinear estimate for the Xs, b spaces associated to the periodic
Airy equation. As a consequence we obtain sharp local well-posedness results for periodic …