Scattering for defocusing energy subcritical nonlinear wave equations
نویسندگان
چکیده
منابع مشابه
Subcritical Scattering for Defocusing Nonlinear Schrödinger Equations
We survey some known results concerning the asymptotic behavior of solutions to defocusing nonlinear Schrödinger equations. In particular, we discuss the H1 scattering theory for intercritical NLS, as well as the scattering theory in weighted spaces for the mass-subcritical case. We also discuss an instance of modified scattering in the long-range case.
متن کاملThe Inverse Scattering Transform for the Defocusing Nonlinear Schrödinger Equations with Nonzero Boundary Conditions
A rigorous theory of the inverse scattering transform for the defocusing nonlinear Schrödinger equation with nonvanishing boundary values q± ≡ q0e± as x → ±∞ is presented. The direct problem is shown to be well posed for potentials q such that q − q± ∈ L1,2(R±), for which analyticity properties of eigenfunctions and scattering data are established. The inverse scattering problem is formulated a...
متن کامل6 Global Well - Posedness and Scattering for the Defocusing Energy - Critical Nonlinear Schrödinger Equation in R
We obtain global well-posedness, scattering, uniform regularity, and global L6t,x spacetime bounds for energy-space solutions to the defocusing energy-critical nonlinear Schrödinger equation in R × R. Our arguments closely follow those in [11], though our derivation of the frequency-localized interaction Morawetz estimate is somewhat simpler. As a consequence, our method yields a better bound o...
متن کاملVortex Splitting in Subcritical Nonlinear Schrödinger Equations
Vortices and axisymmetric vortex rings are considered in the framework of the subcritical nonlinear Schrödinger equations. The higher order nonlinearity present in such systems models many-body interactions in superfluid systems and allows one to study the effects of negative pressure on vortex dynamics. We find the critical pressure for which the straight-line vortex becomes unstable to radial...
متن کاملFinite Energy Travelling Waves for Nonlinear Damped Wave Equations
E(u,ut) = f |Vu|2 + m\u\2 + |ut|2 dx — [ |u|"+1 dx, (1.3) 2 JRn a+ 1 JR„ which represents a Lyapunov function of the problem, i.e., it is decreasing along any nonstationary trajectory of (1.1). Employing the potential-well arguments of PAYNE-SATTINGER [16] one observes that any solution of (1.1) emanating from sufficiently small initial data exists globally for all t e R+ and tends to zero with...
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: Analysis & PDE
سال: 2020
ISSN: 1948-206X,2157-5045
DOI: 10.2140/apde.2020.13.1995