6 citations · 26 across the 15 of their papers we have counts for
15 papers
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 in the critical regime, where with …
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 , where , an…
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 behaves like $\left|x\rig…
Global solutions for -critical nonlinear biharmonic Schrödinger equation
Xuan Liu, Ting Zhang
We consider the nonlinear biharmonic Schrödinger equation in the critical Sobolev space , where , or…
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 where or and . Firstly, we prove local well-posedness in…
On a maximal inequality and its application to SDEs with singular drift
Xuan Liu, Guangyu Xi
In this paper we present a Doob type maximal inequality for stochastic processes satisfying the conditional increment control condition. If we assume, in addition, that the margins…
Sobolev inequalities on product Sierpinski spaces
Xuan Liu, Zhongmin Qian
On fractals, different measures (mutually singular in general) are involved to measure volumes of sets and energies of functions. Singularity of measures brings difficulties in (es…
A uniform approach to soliton cellular automata using rigged configurations
Xuan Liu, Travis Scrimshaw
For soliton cellular automata, we give a uniform description and proofs of the solitons, the scattering rule of two solitons, and the phase shift using rigged configurations in a n…
Parabolic type equations associated with the Dirichlet form on the Sierpinski gasket
Xuan Liu, Zhongmin Qian
By using the analytic tools of Dirichlet forms, we initiate a study of some non-linear parabolic equations on Sierpinski gasket, motivated by modellings of fluid flows along a frac…
A stochastic Pontryagin maximum principle on the Sierpinski gasket
Xuan Liu
In this paper, we consider stochastic control problems on the Sierpinski gasket. An order comparison lemma is derived using heat kernel estimate for Brownian motion on the gasket.…
Backward problems for stochastic differential equations on the Sierpinski gasket
Xuan Liu, Zhongmin Qian
In this paper, we study the non-linear backward problems (with deterministic or stochastic durations) of stochastic differential equations on the Sierpinski gasket. We prove the ex…
On the maximum of a type of random processes
Xuan Liu
We consider a type of random processes which satisfies the conditional increment condition and obtain an estimate for the tail probability and a Doob-type inequality of the maximum…
A Quasi-sure Non-degeneracy Property for the Brownian Rough Path
Horatio Boedihardjo, Xi Geng, Xuan Liu +1
In the present paper, we are going to show that outside a slim set in the sense of Malliavin (or quasi-surely), the signature path (which consists of iterated path integrals in eve…
Maximal Subalgebras for Lie Superalgebras of Cartan Type
Wei Bai, Wende Liu, Xuan Liu +1
The maximal graded subalgebras for four families of Lie superalgebras of Cartan type over a field of prime characteristic are studied. All maximal reducible graded subalgebras are…
Maximal graded subalgebras of Witt and Special superalgebras
Wende Liu, Xuan Liu
This paper has been withdrawn by the author due to that the main results and approaches are closedly parallel to the ones in Lie algebra case.