Infinite-energy solutions to energy-critical nonlinear Schr\"odinger equations in modulation spaces

TL;DR

This paper establishes well-posedness for energy-critical nonlinear Schrödinger equations in modulation spaces, allowing for initial data with infinite mass and energy, using bilinear refinements and specialized function spaces.

Contribution

It introduces new well-posedness results for energy-critical NLS in modulation spaces, extending analysis to infinite-mass and infinite-energy initial data.

Findings

Proves well-posedness for initial data with infinite mass and energy.

Develops bilinear refinements and adapted function spaces for analysis.

Extends the class of initial data for which NLS solutions are well-defined.

Abstract

We prove new well-posedness results for energy-critical nonlinear Schr\"odinger equations in modulation spaces. This covers initial data with infinite mass and energy. The proof is carried out via bilinear refinements and adapted function spaces.