# On Strichartz estimates from decoupling and applications

## TL;DR

This paper derives Strichartz estimates using decoupling techniques under curvature conditions, introduces bilinear refinements, and applies these results to prove local well-posedness for certain nonlinear Schrödinger equations.

## Contribution

It introduces new decoupling-based methods for Strichartz estimates and applies bilinear refinements to nonlinear Schrödinger equations, extending previous results.

## Key findings

- Strichartz estimates obtained from $ ext{ell}^2$-decoupling under curvature conditions
- Bilinear refinements without high-frequency loss
- Local well-posedness for generalized cubic nonlinear Schrödinger equations

## Abstract

Strichartz estimates are derived from $\ell^2$-decoupling for phase functions satisfying a curvature condition. Bilinear refinements without loss in the high frequency are discussed. Estimates are established from uniform curvature generalizing Galilean invariance or from transversality in one dimension. The bilinear refinements are utilized to prove local well-posedness for generalized cubic nonlinear Schr\"odinger equations.