Global solutions and asymptotic behaviors of the Chern–Simons–Dirac equations in R1+1

AbstractThe initial value problem of the Chern–Simons–Dirac equations in one space dimension is studied. We prove the existence of global solution and investigate asymptotic behaviors

Energy Solution to the Chern-Simons-Schrödinger Equations

We prove that the Chern-Simons-Schrödinger system, under the condition of a Coulomb gauge, has a unique local-in-time solution in the energy space . The Coulomb gauge provides elliptic features for gauge fields . The Koch- and Tzvetkov-type Strichartz estimate is applied with Hardy-Littlewood-Sobolev and Wente's inequalities

Reduction of Chern-Simons-Schrödinger Systems in One Space Dimension

We study Chern-Simons-Schrödinger systems in one space dimension. We show that Chern-Simons-Schrödinger and =2 supersymmetric Chern-Simons-Schrödinger equations can be reduced, under the gauge condition A1≡0, to equations of ϕ, ψ only which are coupled cubic Schrödinger systems

Global Strong Solutions to Some Nonlinear Dirac Equations in Super-Critical Space

We study the initial value problem of some nonlinear Dirac equations which are Lmℝ critical. Corresponding to the structure of nonlinear terms, global strong solutions can be obtained in different Lebesgue spaces by using solution representation formula. The uniqueness of weak solutions is proved for the solution U∈L∞0,T; Ym+2ℝ

Existence of Global Solution and Traveling Wave of the Modified Short-Wave Equation

The modified short-wave equation is considered under periodic boundary condition. We prove the global existence of solution with finite energy. We also find traveling wave solutions which is the form of elliptic function

Local and global solutions of the Chern–Simons–Higgs system

AbstractWe study low regularity solutions of the Chern–Simons–Higgs equations. The Lorentz gauge condition makes them hyperbolic equations with the null form. Under the Coulomb gauge condition they are formulated in the hyperbolic equation coupled with elliptic equation. The div–curl decomposition is used in the temporal gauge

Remarks on Chern-Simons-Higgs Equations in R

We prove global existence of solutions to Chern-Simons-Higgs equations under the gauge condition A1=0. We also find stationary solutions