22 citations · 124 across the 23 of their papers we have counts for
15 papers · 1 filter
A remark on the Strichartz inequality in one dimension
Ryan Frier, Shuanglin Shao
In this paper, we study the extremal problem for the Strichartz inequality for the Schrödinger equation on . We show that the solutions to the associated Euler-Lagran…
A remark on the two dimensional water wave problem with surface tension
Shuanglin Shao, Hsi-Wei Shih
We consider the motion of a two-dimensional interface between air (above) and an irrotational, incompressible, inviscid, infinitely deep water (below), with surface tension present…
On smoothness of extremizers of the Tomas-Stein inequality for
Shuanglin Shao, Ming Wang
We prove that the extremizers to the Tomas-Stein inequality for the one dimension sphere are smooth. This is achieved by studying the associated Euler-Lagrange equation.
On one dimensional Quantum Zakharov system
Jin-Cheng Jiang, Chi-Kun Lin, Shuanglin Shao
In this paper, we discuss the properties of one dimensional quantum Zakharov system which describes the nonlinear interaction between the quantum Langmuir and quantum ion-acoustic…
Linear profile decompositions for a family of fourth order Schrödinger equations
Jincheng Jiang, Shuanglin Shao, Betsy Stovall
We establish linear profile decompositions for the fourth order Schrödinger equation and for certain fourth order perturbations of the Schrödinger equation, in dimensions greater t…
On characterization of the sharp Strichartz inequality for the Schrödinger Equation
Jin-Cheng Jiang, Shuanglin Shao
In this paper, we study the extremal problem for the Strichartz inequality for the Schrödinger equation on the ; we provide a new proof to the chara…
On extremisers to a bilinear Strichartz inequality
Shuanglin Shao
In this note, we show that a pair of Gaussian functions are extremisers to a bilinear Strichartz inequality, and unique up to the symmetry group of the inequality.
Nonexistence of soliton-like solutions for defocusing generalized KdV equations
Soonsik Kwon, Shuanglin Shao
In this short note, we consider the global dynamics of the defocusing generalized KdV equations: u_t + u_{xxx} = (|u|^{p-1}u)_x. We use Tao's theorem that the energy moves faster t…
Analyticity of extremisers to the Airy Strichartz inequality
Dirk Hundertmark, Shuanglin Shao
We prove that there exists an extremal function to the Airy Strichartz inequality, by using the linear profile deco…
The linear profile decomposition for the fourth order Schrödinger equation
Jin-Cheng Jiang, Benoit Pausader, Shuanglin Shao
In this paper, we establish the linear profile decomposition for the one dimensional fourth order Schrödinger equation $$ iu_t-μΔu+Δ^2u=0, t\in\mathbb{R}, x\in\mathbb{R}, u(0,x)=f(…
The low regularity global solutions for the critical generalized KdV equation
Changxing Miao, Shuanglin Shao, Yifei Wu +1
We prove that the Cauchy problem of the mass-critical generalized KdV equation is globally well-posed in Sobolev spaces for . Of course, we require that the mass…
On the mass-critical generalized KdV equation
Rowan Killip, Soonsik Kwon, Shuanglin Shao +1
We consider the mass-critical generalized Korteweg--de Vries equation for real-valued functions . We prove that if th…
The mass-critical fourth-order Schrodinger equation in high dimensions
Benoit Pausader, Shuanglin Shao
We prove global wellposedness and scattering for the Mass-critical homogeneous fourth-order Schrodinger equation in high dimensions n>4, for general L^2 initial data in the defocus…
Maximizers for the Strichartz inequalities and the Sobolev-Strichartz inequalities for the Schrödinger equation
Shuanglin Shao
In this paper, we first show that there exists a maximizer for the non-endpoint Strichartz inequalities for the Schrödinger equation in all dimensions based on the recent linear pr…
The linear profile decomposition for the Airy equation and the existence of maximizers for the Airy Strichartz inequality
Shuanglin Shao
In this paper, we establish the linear profile decomposition for the Airy equation with complex or real initial data in , respectively. As an application, we obtain a dichotom…