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<p>We consider the dispersion-generalized KP-II equation on a partially periodic domain in the weakly dispersive regime. We use Fourier decoupling techniques to derive essentially sharp Strichartz estimates. With these in hand, we show that global well-posedness of the quasilinear Cauchy problem in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^2(\mathbb {R}\times \mathbb {T})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>L</mi> <mn>2</mn> </msup> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="double-struck">R</mi> <mo>×</mo> <mi mathvariant="double-struck">T</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>. Finally, we prove a long-time decay property of solutions with small mass by using the Kato smoothing effect in the fractional case.</p>

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Global Results for Weakly Dispersive KP-II Equations on the Cylinder

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月23日

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  • Sebastian Herr,
  • Robert Schippa,
  • Nikolay Tzvetkov

摘要

We consider the dispersion-generalized KP-II equation on a partially periodic domain in the weakly dispersive regime. We use Fourier decoupling techniques to derive essentially sharp Strichartz estimates. With these in hand, we show that global well-posedness of the quasilinear Cauchy problem in \(L^2(\mathbb {R}\times \mathbb {T})\) L 2 ( R × T ) . Finally, we prove a long-time decay property of solutions with small mass by using the Kato smoothing effect in the fractional case.