WELL-POSEDNESS AND BLOW-UP CRITERION FOR A CHERN-SIMONS GAUGED NONLINEAR SCHRÖDINGER EQUATION

doi:10.1007/s10473-026-0207-1

Abstract

Abstract: This paper investigates the Cauchy problem for the Chern-Simons gauged nonlinear Schrödinger equation with a power-type nonlinearity. Previous studies on this equation usually relied on restrictive assumptions, such as radial symmetric initial data or mass-critical exponent ($p=4$). This work overcomes these limitations by employing Kato's theorem, energy method, and an approximation technique. Specifically, for both cases of mass-critical exponent and mass-supercritical exponent ($p>4$), we establish the local well-posedness of the Cauchy problem without the assumption of radial symmetry property to the initial data. Additionally, a sharp threshold is obtained for the global existence and blow-up to time-dependent solutions.

Key words: nonlinear Schrö, dinger equation, well-posedness, blow-up, Chern-Simons term

CLC Number:

35Q40

Qianqian BAI, Yongsheng JIANG, Xiaoguang LI, Jun WANG. WELL-POSEDNESS AND BLOW-UP CRITERION FOR A CHERN-SIMONS GAUGED NONLINEAR SCHRÖDINGER EQUATION[J].Acta mathematica scientia,Series B, 2026, 46(2): 617-641.

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