26 citations · 174 across the 43 of their papers we have counts for
11 papers · 2 filters
Blowup of solutions for a class of the focusing inhomogeneous nonlinear Schrödinger equation
Van Duong Dinh
In this paper, we consider a class of the focusing inhomogeneous nonlinear Schrödinger equation \[ i\partial_t u + Δu + |x|^{-b} |u|^αu = 0, \quad u(0)=u_0 \in H^1(\mathbb{R}^d), \…
Global existence and blowup for a class of the focusing nonlinear Schrödinger equation with inverse-square potential
Van Duong Dinh
We consider a class of the focusing nonlinear Schrödinger equation with inverse-square potential \[ i\partial_t u + Δu -c|x|^{-2}u = - |u|^αu, \quad u(0)=u_0 \in H^1, \quad (t,x)\i…
Energy scattering for a class of the defocusing inhomogeneous nonlinear Schrödinger equation
Van Duong Dinh
In this paper, we consider a class of the defocusing inhomogeneous nonlinear Schrödinger equation \[ i\partial_t u + Δu - |x|^{-b} |u|^αu = 0, \quad u(0)=u_0 \in H^1, \] with $b, α…
Scattering theory in a weighted space for a class of the defocusing inhomogeneous nonlinear Schrödinger equation
Van Duong Dinh
In this paper, we consider the following inhomogeneous nonlinear Schrödinger equation (INLS) \[ i\partial_t u + Δu + μ|x|^{-b} |u|^αu = 0, \quad (t,x)\in \mathbb{R} \times \mathbb{…
Global existence for the defocusing mass-critical nonlinear fourth-order Schrödinger equation below the energy space
Van Duong Dinh
In this paper, we consider the defocusing mass-critical nonlinear fourth-order Schrödinger equation. Using the -method combined with the interaction Morawetz estimate, we prove…
On the focusing mass-critical nonlinear fourth-order Schrödinger equation below the energy space
Van Duong Dinh
In this paper, we consider the focusing mass-critical nonlinear fourth-order Schrödinger equation. We prove that blowup solutions to this equation with initial data in $H^γ(\mathbb…
Global existence and scattering for a class of nonlinear fourth-order Schrödinger equation below the energy space
Van Duong Dinh
In this paper, we consider a class of nonlinear fourth-order Schrödinger equation, namely \[ \left\{ \begin{array}{rcl} i\partial_t u +Δ^2 u &=&-|u|^{ν-1} u, \quad 1+ \frac{8}{d}<ν…
Global in time Strichartz estimates for the fractional Schrödinger equations on asymptotically Euclidean manifolds
Van Duong Dinh
In this paper, we prove global in time Strichartz estimates for the fractional Schrödinger operators, namely with and $Λ_g:=\sqrt{-…
Well-posedness, regularity and ill-posedness for the nonlinear fourth-order Schrödinger equation
Van Duong Dinh
We prove the local well-posedness for the nonlinear fourth-order Schrödinger equation (NL4S) in Sobolev spaces. We also studied the regularity of solutions in the sub-critical case…
Global well-posedness for a -critical nonlinear higher-order Schrödinger equation
Van Duong Dinh
We prove the global well-posedness for a -critical defocusing cubic higher-order Schrödinger equation, namely \[ i\partial_t u + Λ^k u = -|u|^2 u, \] where and $…
On the Cauchy problem for the nonlinear semi-relativistic equation in Sobolev spaces
Van Duong Dinh
We proved the local well-posedness for the power-type nonlinear semi-relativistic or half-wave equation (NLHW) in Sobolev spaces. Our proofs mainly bases on the contraction mapping…