Local existence, global existence, and scattering for the nonlinear Schrödinger equation
نویسندگان
چکیده
منابع مشابه
Existence, stability, and scattering of bright vortices in the cubic-quintic nonlinear Schrödinger equation
We revisit the topic of the existence and azimuthal modulational stability of solitary vortices (alias vortex solitons) in the twodimensional (2D) cubic–quintic nonlinear Schrödinger equation. We develop a semi-analytical approach, assuming that the vortex soliton is relatively narrow, which allows one to effectively split the full 2D equation into radial and azimuthal 1D equations. A variation...
متن کامل2 00 6 Global Existence and Scattering for Rough Solutions to Generalized Nonlinear Schrödinger Equations On
We consider the Cauchy problem for a family of semilinear defocusing Schrödinger equations with monomial nonlinearities in one space dimension. We establish global well-posedness and scattering. Our analysis is based on a four-particle interaction Morawetz estimate giving a priori Lt,x spacetime control on solutions.
متن کامل2 00 4 Global Existence and Scattering for Rough Solutions of a Nonlinear Schrödinger Equation on R 3
We prove global existence and scattering for the defocusing, cubic nonlinear Schrödinger equation in H s (R 3) for s > 4 5. The main new estimate in the argument is a Morawetz-type inequality for the solution φ. This estimate bounds φ(x, t) L 4 x,t (R 3 ×R) , whereas the well-known Morawetz-type estimate of Lin-Strauss controls ∞ 0 R 3 (φ(x,t)) 4 |x| dxdt.
متن کاملGlobal existence and scattering for the nonlinear Schrödinger equation on Schwarzschild manifolds
We consider the nonlinear Schrödinger equation with a pure power repulsive nonlinearity on Schwarzschild manifolds. Equations of this type arise when a nonlinear wave equation on a Schwarzschild manifold is written in Hamiltonian form, cf. [2], [10]. For radial solutions with sufficiently localized initial data, we obtain global existence, L estimates, and the existence and asymptotic completen...
متن کاملLocal and Global Existence for an Aggregation Equation
The purpose of this work is to develop a satisfactory existence theory for a general class of aggregation equations. An aggregation equation is a non-linear, non-local partial differential equation that is a regularization of a backward diffusion process. The non-locality arises via convolution with a potential. Depending on how regular the potential is, we prove either local or global existenc...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications in Contemporary Mathematics
سال: 2017
ISSN: 0219-1997,1793-6683
DOI: 10.1142/s0219199716500383