Abstract
We study the nonlinear Schrödinger equation with initial data in $ \mathcal Z ^s_p(\mathbb R^d)=\dot{H}^s(\mathbb R^d)\cap L^p(\mathbb R^d)$, where $0 < s < \min\{d/2,1\}$ and $2 < p < 2d/(d-2s)$. After showing that the linear Schrödinger group is well-defined in this space, we prove local well-posedness in the whole range of parameters $s$ and $p$. The precise properties of the solution depend on the relation between the power of the nonlinearity and the integrability $p$. Finally, we present a global existence result for the defocusing cubic equation in dimension three for initial data with infinite mass and energy, using a variant of the Fourier truncation method.
Citation
Vanessa Barros. Simão Correia. Filipe Oliveira. "On the nonlinear Schrödinger equation in spaces of infinite mass and low regularity." Differential Integral Equations 35 (7/8) 371 - 392, July/August 2022. https://doi.org/10.57262/die035-0708-371
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