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<p>We examine well-posedness issues for a magnetic nonlinear inhomogeneous Schrödinger equation in three spatial dimensions. First, we develop a local theory in the energy space. Second, under certain sufficient conditions, we analyze the finite-time blow-up of focusing mass-supercritical solutions. Lastly, we establish the energy scattering of defocusing inter-critical global solutions.</p>

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A Note on the Magnetic INLS in Three Space Dimensions

  • 期刊论文

  • 发表日期：

    2026年1月16日

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  • Tarek Saanouni

摘要

We examine well-posedness issues for a magnetic nonlinear inhomogeneous Schrödinger equation in three spatial dimensions. First, we develop a local theory in the energy space. Second, under certain sufficient conditions, we analyze the finite-time blow-up of focusing mass-supercritical solutions. Lastly, we establish the energy scattering of defocusing inter-critical global solutions.