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This paper treats an initial value problem of a system of nonlinear Schrödinger equations with critical dissipative power nonlinearities. Our aim is to show that optimal \(L^{\infty }\) -decay rate of the solutions is \(t^{-1/2} (\ln t)^{-1/2}\) . In other words, if a solution \(\mathbf {u}(t)\) satisfies \(\|\mathbf {u}(t)\|_{L^{\infty }} = o(t^{-1/2} (\ln t)^{-1/2})\) as \(t \to \infty \) , then \(\mathbf {u}(t,x) \equiv 0\) .

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Optimal \(L^{\infty }\) -Decay Rate of Solutions to a Dissipative Nonlinear Schrödinger Equation System

  • 会议论文

  • 发表日期：

    2025年

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  • Naoyasu Kita,
  • Yoshihisa Nakamura,
  • Yuji Sagawa

摘要

This paper treats an initial value problem of a system of nonlinear Schrödinger equations with critical dissipative power nonlinearities. Our aim is to show that optimal \(L^{\infty }\) -decay rate of the solutions is \(t^{-1/2} (\ln t)^{-1/2}\) . In other words, if a solution \(\mathbf {u}(t)\) satisfies \(\|\mathbf {u}(t)\|_{L^{\infty }} = o(t^{-1/2} (\ln t)^{-1/2})\) as \(t \to \infty \) , then \(\mathbf {u}(t,x) \equiv 0\) .