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<p>We revisit the local well-posedness for the KP-I equation. We obtain unconditional local well-posedness in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(H^{s,0}({\mathbb R}^2)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>H</mi> <mrow> <mi>s</mi> <mo>,</mo> <mn>0</mn> </mrow> </msup> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mn>2</mn> </msup> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> for <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(s&gt;3/4\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>s</mi> <mo>&gt;</mo> <mn>3</mn> <mo stretchy="false">/</mo> <mn>4</mn> </mrow> </math></EquationSource> </InlineEquation> and unconditional global well-posedness in the energy space. We also prove the global existence of perturbations with finite energy of non decaying smooth global solutions.</p>

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On the Well-Posedness of the KP-I Equation

  • 期刊论文

  • 发表日期：

    2026年3月16日

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  • Zihua Guo,
  • Luc Molinet

摘要

We revisit the local well-posedness for the KP-I equation. We obtain unconditional local well-posedness in \(H^{s,0}({\mathbb R}^2)\) H s , 0 ( R 2 ) for \(s>3/4\) s > 3 / 4 and unconditional global well-posedness in the energy space. We also prove the global existence of perturbations with finite energy of non decaying smooth global solutions.