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<p>We investigate the dispersive behaviors of Schrödinger and wave equations with partial inverse-square potentials. The crucial aspect in establishing Strichartz estimates lies in constructing the spectral measure for a Schrödinger operator with partial inverse-square potentials in <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12220_2025_1907_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="35" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {R}^{2+n}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mrow> <mn>2</mn> <mo>+</mo> <mi>n</mi> </mrow> </msup> </math></EquationSource> </InlineEquation>. This approach differs from the perturbation argument presented in Burq et al. (J Funct Anal 203:519–549, 2003) and Burq et al. (Indiana Univer Math J 53:1665–1680, 2004) because the potentials have no decay in certain directions. As applications, we prove the Strichartz estimates for Schrödinger and wave equations associated with two-particle interaction Schrödinger operators.</p>

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Strichartz Estimates for Dispersive Equations with Partial Inverse-Square Potentials

  • 期刊论文

  • 发表日期：

    2025年2月6日

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  • Fang Zhang,
  • Junyong Zhang

摘要

We investigate the dispersive behaviors of Schrödinger and wave equations with partial inverse-square potentials. The crucial aspect in establishing Strichartz estimates lies in constructing the spectral measure for a Schrödinger operator with partial inverse-square potentials in \(\mathbb {R}^{2+n}\) R 2 + n . This approach differs from the perturbation argument presented in Burq et al. (J Funct Anal 203:519–549, 2003) and Burq et al. (Indiana Univer Math J 53:1665–1680, 2004) because the potentials have no decay in certain directions. As applications, we prove the Strichartz estimates for Schrödinger and wave equations associated with two-particle interaction Schrödinger operators.