Local Well-Posedness of the Periodic Nonlinear Schrödinger Equation with a Quadratic Nonlinearity u ¯ 2 in Negative Sobolev Spaces.

We study low regularity local well-posedness of the nonlinear Schrödinger equation (NLS) with the quadratic nonlinearity  u ¯ 2 , posed on one-dimensional and two-dimensional tori. While the relevant bilinear estimate with respect to the X s , b -space is known to fail when the regularity s is below some threshold value, we establish local well-posedness for such low regularity by introducing modifications on the X s , b -space. © The Author(s) 2023.

Citation

Ruoyuan Liu. Local Well-Posedness of the Periodic Nonlinear Schrödinger Equation with a Quadratic Nonlinearity u ¯ 2 in Negative Sobolev Spaces. Journal of dynamics and differential equations. 2025;37(1):509-538

PMID: 39974333

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