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arXiv · 2412.19714

Fractional nonlinear Schrödinger and Hartree equations in modulation spaces

Divyang G. Bhimani·Diksha Dhingra·Vijay Kumar Sohani
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Abstract

We establish global well-posedness for the mass subcritical nonlinear fractional Schrödinger equation $$iu_t - (-Δ)^\fracβ{2} u+F(u)=0$$ having radial initial data in modulation spaces $M^{p,\frac{p}{p-1}}(\mathbb R^n)$ for $n \geq 2, p>2$ and $p$ sufficiently close to $2.$ The nonlinearity $F(u)$ is either of power-type $F(u)=\pm (|u|^αu)\; (0<α<2β/ n)$ or Hartree-type $(|x|^{-ν} \ast |u|^{2})u \; (0<ν<\min\{β,n\}).$ Our order of dispersion $β$ lies in $(2n/ (2n-1), 2).$

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Divyang G. Bhimani, Diksha Dhingra, Vijay Kumar Sohani. 2025-03-10. Fractional nonlinear Schrödinger and Hartree equations in modulation spaces. https://arxiv.org/abs/2412.19714

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