相关论文: Blow-up for the 3D intercritical inhomogeneous NLS…

We consider the inhomogeneous nonlinear Schr\"odinger equation with inverse-square potential in $\mathbb{R}^N$ $$ i u_t + \mathcal{L}_a u+\lambda |x|^{-b}|u|^\alpha u = 0,\;\;\mathcal{L}_a=\Delta -\frac{a}{|x|^2}, $$ where $\lambda=\pm1$,…

We consider the focusing cubic nonlinear Schr\"odinger equation with inverse-square potential in three space dimensions. We identify a sharp threshold between scattering and blowup, establishing a result analogous to that of Duyckaerts,…

In this paper we consider the inhomogeneous nonlinear Schr\"odinger (INLS) equation \begin{align}\label{inls} i \partial_t u +\Delta u +|x|^{-b} |u|^{2\sigma}u = 0, \,\,\, x \in \mathbb{R}^N \end{align} with $N\geq 3$. We focus on the…

We study the nonlinear Schr\"odinger equation with an inverse-square potential in dimensions $3\leq d \leq 6$. We consider both focusing and defocusing nonlinearities in the mass-supercritical and energy-subcritical regime. In the focusing…

We study minimal mass blow-up solutions of the focusing $L^2$ critical nonlinear Schr\"odinger equation with inverse-square potential, \[ i\partial_t u + \Delta u + \frac{c}{|x|^2}u+|u|^{\frac{4}{N}}u = 0, \] with $N\geqslant 3$ and…

We investigate the blow-up for a fourth-order Schr\"odinger equation with a mas-critical focusing inhomogeneous nonlinearity. We prove the finite/infinite-time blow-up of non-radial solutions with negative energy. Our result serves as a…

In this paper, we consider the 3d cubic focusing inhomogeneous nonlinear Schr\"{o}dinger equation with a potential $$ iu_{t}+\Delta u-Vu+|x|^{-b}|u|^{2}u=0,\;\;(t,x) \in {{\bf{R}}\times{\bf{R}}^{3}}, $$ where $0<b<1$. We first establish…

We consider the $L^2$ critical inhomogeneous nonlinear Schr\"odinger (INLS) equation in $\mathbb{R}^N$ $$ i \partial_t u +\Delta u +|x|^{-b} |u|^{\frac{4-2b}{N}}u = 0, $$ where $N\geq 1$ and $0<b<2$. We prove that if $u_0\in…

We consider the inhomogeneous nonlinear Schr\"odinger equation (INLS) in $\mathbb{R}^N$, $N \geq 1$, $$i \partial_t u + \Delta u + |x|^{-b} |u|^{p-1}u = 0,$$ with finite-variance initial data $u_0 \in H^1(\mathbb{R}^N)$. We extend the…

We investigate the following inhomogeneous nonlinear Schr\"odinger equation in the radial regime, featuring a focusing energy-critical nonlinearity and a defocusing perturbation: $$ i\partial_t u +\Delta u =|x|^{-a} |u|^{p-2} u - |x|^{-b}…

In this paper, we prove a refined version of a compactness lemma and we use it to establish mass-concentration for the focusing nonlinear Schr\"{o}dinger equation with an inverse-square potential.

We consider the defocusing energy-critical nonlinear Schr\"odinger equation with inverse-square potential $iu_t = -\Delta u + a|x|^{-2}u + |u|^4u$ in three space dimensions. We prove global well-posedness and scattering for $a>-\frac14…

We consider the nonlinear Schr\"odinger equation $iu_t=-\Delta u-|u|^{p-1}u$ in dimension $N\geq 3$ in the $L^2$ super critical range $1+\frac{4}{N}<p<\frac{N+2}{N-2}$. The corresponding scaling invariant space is $\dot{H}^{s_c}$ with…

In this paper, we investigate the blow-up phenomenon of the $H^2$ norm of solutions to the inhomogeneous biharmonic Schrodinger equation in two distinct scenarios. First, we consider the case of negative energy, analyzing separately the…

In this paper, we study the Cauchy problem for the focusing inhomogeneous nonlinear Schr\"{o}dinger equation with inverse-square potential \[iu_{t} +\Delta u-c|x|^{-2}u+|x|^{-b} |u|^{\sigma } u=0,\; u(0)=u_{0} \in H_{c}^{1},\;(t,x)\in…

This paper is dedicated to the blow-up solution for the divergence Schr\"{o}dinger equations with inhomogeneous nonlinearity (dINLS for short) \[i\partial_tu+\nabla\cdot(|x|^b\nabla u)=-|x|^c|u|^pu,\quad\quad u(x,0)=u_0(x),\] where…

In this paper, we consider the mass-critical nonlinear Schr\"odinger equation in one dimension. Ogawa--Tsutsumi [19] proved a blow-up result for negative energy solution by using a scaling argument for initial data. By the reason, the…

We consider a class of $L^2$-supercritical inhomogeneous nonlinear Schr\"odinger equations with potential in three dimensions \[ i\partial_t u + \Delta u - V u = \pm |x|^{-b} |u|^\alpha u, \quad (t,x) \in \mathbb{R} \times \mathbb{R}^3, \]…

For the 3d cubic nonlinear Schr\"odinger (NLS) equation, which has critical (scaling) norms $L^3$ and $\dot H^{1/2}$, we first prove a result establishing sufficient conditions for global existence and sufficient conditions for finite-time…

We consider the $L^2$-critical NLS with inverse-square potential $$ i \partial_t u +\Delta u + c|x|^{-2} u = -|u|^{\frac{4}{d}} u, \quad u(0) = u_0, \quad (t,x) \in \mathbb{R}^+ \times \mathbb{R}^d, $$ where $d\geq 3$ and $c\ne 0$ satisfies…