Results 1 
9 of
9
Low regularity local wellposedness of the derivative nonlinear Schrdinger equation with periodic initial data
 SIAM J. Math. Anal
"... Abstract. The Cauchy problem for the derivative nonlinear Schrödinger equation with periodic boundary condition is considered. Local wellposedness for data u0 in the space b Hs r (T), defined by the norms ‖u0 ‖ bH s r (T) = ‖〈ξ〉s bu0‖ ℓ r ′ ξ is shown in the parameter range s ≥ 1 4, 2> r>. T ..."
Abstract

Cited by 25 (1 self)
 Add to MetaCart
(Show Context)
Abstract. The Cauchy problem for the derivative nonlinear Schrödinger equation with periodic boundary condition is considered. Local wellposedness for data u0 in the space b Hs r (T), defined by the norms ‖u0 ‖ bH s r (T) = ‖〈ξ〉s bu0‖ ℓ r ′ ξ is shown in the parameter range s ≥ 1 4, 2> r>. The proof is based on an 2 3 adaptation of the gauge transform to the periodic setting and an appropriate variant of the Fourier restriction norm method. 1. Introduction and
Invariant weighted Wiener measures and almost sure global wellposedness for the periodic derivative
 NLS, J. Eur. Math. Soc
"... Abstract. In this paper we construct an invariant weighted Wiener measure associated to the periodic derivative nonlinear Schrödinger equation in one dimension and establish global wellposedness for data living in its support. In particular almost surely for data in a FourierLebesgue space FL s,r ..."
Abstract

Cited by 19 (6 self)
 Add to MetaCart
(Show Context)
Abstract. In this paper we construct an invariant weighted Wiener measure associated to the periodic derivative nonlinear Schrödinger equation in one dimension and establish global wellposedness for data living in its support. In particular almost surely for data in a FourierLebesgue space FL s,r (T) with s ≥ 1 2 , 2 < r < 4, (s − 1)r < −1 and scaling like H 1 2 − (T), for small > 0. We also show the invariance of this measure.
Absolute continuity of Brownian bridges under certain gauge transformations
, 2011
"... ar ..."
(Show Context)
Remark on wellposedness for the fourth order nonlinear Schrödinger type equation
 Proc. Amer. Math. Soc
"... ar ..."
(Show Context)
Global wellposedness for Schrödinger equation with derivative in H 2
 R), J. Diff. Eq
, 2011
"... ar ..."
(Show Context)
GLOBAL WELLPOSEDNESS FOR THE NONLINEAR SCHRÖDINGER EQUATION WITH DERIVATIVE IN ENERGY SPACE
"... ar ..."
3 WELLPOSEDNESS IN ENERGY SPACE FOR THE PERIODIC MODIFIED BENJAMINONO EQUATION
"... ar ..."
(Show Context)