相关论文: A Liouville theorem for the Chern--Simons--Schr{\"…
In this paper we prove a rigidity result for a solution to the non self-dual Chern--Simons--Schr{\"o}dinger equation at the level of the soliton.
We consider the self-dual Chern-Simons-Schr\"odinger equation (CSS) under equivariant symmetry, which is a $L^{2}$-critical equation. It is known that (CSS) admits solitons and finite-time blow-up solutions. In this paper, we show soliton…
In this paper we prove a sequential convergence result for blowup solutions to the $m$-equivariant, self-dual Chern--Simons--Schr{\"o}dinger equation. We show that if $u$ has mass less than twice the mass of the soliton, a blowup solution…
I analyze the one-dimensional, cubic Schr\"odinger equation, with nonlinearity constructed from the current density, rather than, as is usual, from the charge density. A soliton solution is found, where the soliton moves only in one…
We consider the Dunne-Jackiw-Pi-Trugenberger model of a U(N) Chern-Simons gauge theory coupled to a nonrelativistic complex adjoint matter on noncommutative space. Soliton configurations of this model are related the solutions of the chiral…
We study a gauged Chern-Simons-CP(1) system. We show that contrary to previous claims the model in the absences of a potential term cannot support finite size soliton solution in $R^2$.
In the paper, a Liouville theorem for mild bounded ancient solutions to the 2D Navier-Stokes equations in half space has been proven.
We are concerned with a skew-symmetric singular Liouville system arising in non-relativistic Chern-Simons theory. Based on its variational structure, we establish existence and multiplicity results. Since the energy functional is…
We study the Derivative Nonlinear Schr\"odinger equation for generic initial data in a weighted Sobolev space that can support bright solitons (but exclude spectral singularities). Drawing on previous well-posedness results, we give a full…
A Chern-Simons gauged Nonlinear Schr\"odinger Equation is derived from the continuous Heisenberg model in 2+1 dimensions. The corresponding planar magnets can be analyzed whithin the anyon theory. Thus, we show that static magnetic vortices…
In this work, we employ the $\bar{\partial}$ steepest descent method in order to study the Cauchy problem of the cgNLS equations with initial conditions in weighted Sobolev space $H^{1,1}(\mathbb{R})=\{f\in L^{2}(\mathbb{R}): f',xf\in…
In this paper, we prove the asymptotic stability of the family of solitons of the Benjamin-Ono equation in the energy space. The proof is based on a Liouville property for solutions close to the solitons for this equation, in the spirit of…
We study one- and two-soliton solutions of noncommutative Chern-Simons theory coupled to a nonrelativistic or a relativistic scalar field. In the nonrelativistic case, we find a tower of new stationary time-dependent solutions, all with the…
We establish a Liouville theorem for bounded mild ancient solutions to the axi-symmetric incompressible Navier-Stokes equations on $(-\infty, 0] \times (\mathbb{R}^2 \times \mathbb{T}^1)$. This is a step forward to completely solve the…
We establish the asymptotic stability of smooth solitons and multi-solitons for the Camassa-Holm (CH) equation in the energy space $H^1(\R)$. We show that solutions initially close to a soliton converge, up to translation, weakly in…
Liouville theorems for scaling invariant nonlinear elliptic systems (saying that the system does not possess nontrivial entire solutions) guarantee a priori estimates of solutions of related, more general systems. Assume that $p=2q+3>1$ is…
We study $SU(2)$ Chern-Simons theories at level $k$ coupled to a scalar on $T^2\times \mathbb{R}$ at large baryon number. We find a homogeneous but anisotropic ground state configuration for any values of $k$ on the IR fixed-point of those…
We compute explicitly the Schr\"odinger picture space of states of SU(2) Chern-Simons theory on $T^2\times R$ in the presence of temporal Wilson lines. Relation with Friedan-Shenker bundle of conformal field theory and the existence of a…
We give a proof of the soliton resolution conjecture for the Benjamin--Ono equation, namely every solution with sufficiently regular and decaying initial data can be written as a finite sum of soliton solutions with different velocities up…
We study the triviality of the solutions of weighted superlinear heat equations on Riemannian manifolds with nonnegative Ricci tensor. We prove a Liouville--type theorem for solutions bounded from below with nonnegative initial data, under…