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We consider the Cauchy problem for a system of nonlinear Schrödinger equations with derivative nonlinearity. By using the energy method, we prove the local well-posedness in the Sobolev space for this system. The energy structure of this system depends on coefficients in linear terms and nonlinear terms. In particular, we give a condition for the coefficients in nonlinear terms that the local well-posedness holds regardless of the coefficients of linear terms.

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Well-Posedness for a System of Nonlinear Schrödinger Equations with Derivative Nonlinearity via the Energy Method

  • 会议论文

  • 发表日期：

    2025年

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  • Hiroyuki Hirayama,
  • Shinya Kinoshita,
  • Mamoru Okamoto

摘要

We consider the Cauchy problem for a system of nonlinear Schrödinger equations with derivative nonlinearity. By using the energy method, we prove the local well-posedness in the Sobolev space for this system. The energy structure of this system depends on coefficients in linear terms and nonlinear terms. In particular, we give a condition for the coefficients in nonlinear terms that the local well-posedness holds regardless of the coefficients of linear terms.