$H_x^s\times H_x^s$ scattering theory for a weighted gradient system of 3D radial defocusing NLS

Abstract

In this paper, using $I$-method, we establish $H_x^s\times H_x^s$ scattering theories for the following Cauchy problem \begin{equation*} \left\{ \begin{array}{lll} iu_t+Δu=λ|v|^2u,\quad iv_t+Δv=μ|u|^2v,\quad x\in \mathbb{R}^3,\ t>0,\\ u(x,0)=u_0(x),\quad v(x,0)=v_0(x),\quad x\in \mathbb{R}^3. \end{array}\right. \end{equation*} Here $\lambda >0$, $\mu >0$, $(u_0,v_0)\in H_x^s({\mathbb{R}}^3)\times H_x^s({\mathbb{R}}^3)$ and $\frac{1}{2}<s<1$.

16pages

References in corpus (2)

• Large global solutions for nonlinear Schrödinger equations III, energy-supercritical cases
• Critical exponents line, scattering thoeries for a weighted gradient system of semilinear Schrodinger equations