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<p>In this paper, we investigate the dynamics of normalized ground states for the focusing <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>-supercritical nonlinear Schrödinger equation (NLSE) with a point interaction in dimension two. First, based on Pohozaev manifold and rearrangement technique, we show that all normalized ground states corresponding to local minima of the associated energy functional exist. Then, we establish a new blow-up criterion, which is related to normalized ground states, and obtain the blow-up results by using the localized Virial estimates. Moreover, we show that the standing waves corresponding to normalized ground states are strongly unstable.</p>

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Dynamics of normalized ground states for the NLSE with a point interaction in dimension two

  • 期刊论文

  • 发表日期：

    2026年4月22日

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  • Yingxin Duan,
  • Guoqing Zhang

摘要

In this paper, we investigate the dynamics of normalized ground states for the focusing \(L^{2}\) L 2 -supercritical nonlinear Schrödinger equation (NLSE) with a point interaction in dimension two. First, based on Pohozaev manifold and rearrangement technique, we show that all normalized ground states corresponding to local minima of the associated energy functional exist. Then, we establish a new blow-up criterion, which is related to normalized ground states, and obtain the blow-up results by using the localized Virial estimates. Moreover, we show that the standing waves corresponding to normalized ground states are strongly unstable.