<p>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 (<i>p</i> = 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 (<i>p</i> &gt; 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.</p>

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Well-posedness and blow-up criterion for a Chern-Simons gauged nonlinear Schrödinger equation

  • Qianqian Bai,
  • Yongsheng Jiang,
  • Xiaoguang Li,
  • Jun Wang

摘要

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.