Xuan Liu

activity

20092021

most citedBackward problems for stochastic differential equations on the Sierpinski gasket

6 citations · 26 across the 15 of their papers we have counts for

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5 papers · 1 filter

math.AP2021

Global existence and asymptotics for the modified two-dimensional Schrödinger equation in the critical regime

Xuan Liu, Ting Zhang

We study the asymptotic behavior of the modified two-dimensional Schrödinger equation $(D_{t} - F (D)) u = λ ∣ u ∣ u$ in the critical regime, where $λ \in C$ with $Im λ \geq 0$ …

math.AP2021

Modified scattering for the one-dimensional Schrödinger equation with a subcritical dissipative nonlinearity

Xuan Liu, Ting Zhang

We study the asymptotic behavior in time of solutions to the one dimensional nonlinear Schrödinger equation with a subcritical dissipative nonlinearity $λ ∣ u ∣^{α} u$ , where $0 < α < 2$ , an…

math.AP2021★ 3 cited

Bilinear Strichartz's type estimates in Besov spaces with application to inhomogeneous nonlinear biharmonic Schrödinger equation

Xuan Liu, Ting Zhang

In this paper, we consider the well-posedness of the inhomogeneous nonlinear biharmonic Schrödinger equation with spatial inhomogeneity coefficient $K (x)$ behaves like $\left|x\rig…

math.AP2021

Global solutions for $H^{s}$ -critical nonlinear biharmonic Schrödinger equation

Xuan Liu, Ting Zhang

We consider the nonlinear biharmonic Schrödinger equation $i \partial_{t} u + (Δ^{2} + μ Δ) u + f (u) = 0, (BNLS)$ in the critical Sobolev space $H^{s} (R^{N})$ , where $N \geq 1$ , $μ = 0$ or…

math.AP2020★ 1 cited

Local well-posedness and finite time blowup for fourth-order Schrödinger equation with complex coefficient

Xuan Liu, Ting Zhang

We consider the fourth-order Schrödinger equation $i \partial_{t} u + Δ^{2} u + μ Δ u + λ ∣ u ∣^{α} u = 0,$ where $α > 0, μ = \pm 1$ or $0$ and $λ \in C$ . Firstly, we prove local well-posedness in…

Global existence and asymptotics for the modified two-dimensional Schrödinger equation in the critical regime

Modified scattering for the one-dimensional Schrödinger equation with a subcritical dissipative nonlinearity

Bilinear Strichartz's type estimates in Besov spaces with application to inhomogeneous nonlinear biharmonic Schrödinger equation

Global solutions for Hs-critical nonlinear biharmonic Schrödinger equation

Local well-posedness and finite time blowup for fourth-order Schrödinger equation with complex coefficient

Global solutions for $H^{s}$ -critical nonlinear biharmonic Schrödinger equation