Nonlinear smoothing implies improved lower bounds on the radius of spatial analyticity for nonlinear dispersive equations

2025/07/17 by Mikaela Baldasso, Baldasso, Mikaela, Simão Correia +1
Earth and Planetary Sciences · #Analysis of PDEs (math.AP) #FOS: Mathematics #Meteorological Phenomena and Simulations #Ocean Waves and Remote Sensing

paper · pdf · doi:10.48550/arxiv.2507.13083

openalex publication_date 2025/07/17 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28

Abstract

We provide a roadmap to establish improved lower bounds on the decay rate of the uniform radius of analyticity σ(T) for a given nonlinear dispersive equation, reducing the problem to the derivation of nonlinear smoothing estimates with a specific distribution of extra derivatives. We apply this strategy for both the defocusing generalized KdV and the nonlinear Schrödinger equations with odd pure-power nonlinearity. For both equations, we reach the lower bound σ(T)\gtrsim T^-(1)/(2)-ε, for any ε>0, thus improving all available results in the current literature.

Citations

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Related

• On the radius of spatial analyticity for defocusing nonlinear Schrödinger equations
• Nonlinear smoothing for dispersive PDE: a unified approach
• On the radius of spatial analyticity for cubic nonlinear Schrödinger equation
• Sharp local well-posedness and nonlinear smoothing for dispersive equations through frequency-restricted estimates
• Global dispersive estimates for defocusing nonlinear Schrodinger equations