ON THE CAUCHY PROBLEM FOR A DERIVATIVE NONLINEAR SCHRÖDINGER EQUATION WITH NONVANISHING BOUNDARY CONDITIONS

Next, we also want to point out that the nonlinear theory yields interesting and difficult new problems. There are many interesting examples, for instance in multi- phase

Local energy decay, damped wave equation, Mourre’s commutators method, non- selfadjoint operators, resolvent

The strategy of Ebin & Marsden [20] to solve the well-posedness problem for the Euler equation was first to recast the equation as an ODE on some approximating Hilbert manifolds

2 Key words; anyon, Haldane statistics, low temperature kinetic theory, quantum Boltzmann equation.... Here dω corresponds to the Lebesgue probability measure on

Dinh, Global existence for the defocusing mass-critical nonlinear fourth-order Schr¨ odinger equation below the energy space, preprint (2017).. Papanicolaou, Self-focusing with

Concerning the Cauchy problem for the hydrodynamical Landau-Lifshitz equation, the main difficulty is to establish the continuity with respect to the initial datum in the energy space

Robbiano, Local well-posedness and blow up in the energy space for a class of L2 critical dispersion generalized Benjamin-Ono equations, Ann. Henri Poincar´

for the generalized Korteweg-de Vries (gKdV) equation and adapted by El Dika and Molinet in [3] and [2] for the Camassa-Holm (CH) equation, we prove here the stability of the sum of