A sharp scattering threshold level for mass-subcritical nonlinear Schrödinger system
نویسندگان
چکیده
In this paper, we consider the quadratic nonlinear Schrodinger system in three space dimensions. Our aim is to obtain sharp scattering criteria. Because of mass-subcritical nature, it difficult do so terms conserved quantities. The corresponding single equation studied by second author and a criterion established introducing distance from trivial solution, zero solution. By structure nonlinearity are dealing with, admits solution which pair function linear flow. Taking fact into account, introduce new optimizing quantity give it.
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 کامل0 A pr 2 00 7 SHARP THRESHOLDS OF BLOW - UP AND GLOBAL EXISTENCE FOR THE COUPLED NONLINEAR SCHRÖDINGER SYSTEM
In this paper, we establish two new types of invariant sets for the coupled nonlinear Schrödinger system on R, and derive two sharp thresholds of blow-up and global existence for its solution. Some analogous results for the nonlinear Schrödinger system posed on the hyperbolic space H and on the standard 2-sphere S are also presented. Our arguments and constructions are improvements of some prev...
متن کاملExistence of Solutions for a Modified Nonlinear Schrödinger System
We are concerned with the followingmodified nonlinear Schrödinger system: −Δu+u−(1/2)uΔ(u2) = (2α/(α+β))|u||V|u, x ∈ Ω, −ΔV+V−(1/2)VΔ(V2) = (2β/(α+β))|u||V|V, x ∈ Ω, u = 0, V = 0, x ∈ ∂Ω, whereα > 2, β > 2, α+β < 2⋅2, 2∗ = 2N/(N−2) is the critical Sobolev exponent, andΩ ⊂ RN (N ≥ 3) is a bounded smooth domain. By using the perturbationmethod, we establish the existence of both positive and nega...
متن کاملOn a class of nonlinear fractional Schrödinger-Poisson systems
In this paper, we are concerned with the following fractional Schrödinger-Poisson system: (−∆s)u + V (x)u + φu = m(x)|u|q−2|u|+ f(x,u), x ∈ Ω, (−∆t)φ = u2, x ∈ Ω, u = φ = 0, x ∈ ∂Ω, where s,t ∈ (0,1], 2t + 4s > 3, 1 < q < 2 and Ω is a bounded smooth domain of R3, and f(x,u) is linearly bounded in u at infinity. Under some assumptions on m, V and f we obtain the existence of non-trivial so...
متن کاملṕ Estimates for the Schrödinger Equation on the Line and Inverse Scattering for the Nonlinear Schrödinger Equation with a Potential ∗
In this paper I prove a L − L estimate for the solutions of the one–dimensional Schrödinger equation with a potential in Lγ where in the generic case γ > 3/2 and in the exceptional case (i.e. when there is a half–bound state of zero energy) γ > 5/2. I use this estimate to construct the scattering operator for the nonlinear Schrödinger equation with a potential. I prove moreover, that the low–en...
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: Discrete and Continuous Dynamical Systems
سال: 2021
ISSN: ['1553-5231', '1078-0947']
DOI: https://doi.org/10.3934/dcds.2020323