Well-posedness for good Boussinesq equations subject to quasi-periodic initial data

TL;DR

This paper proves local well-posedness for the good Boussinesq equation with quasi-periodic initial data, demonstrating existence, uniqueness, and an exponentially decaying Fourier expansion of solutions.

Contribution

It introduces a novel iterative and combinatorial approach to establish well-posedness for quasi-periodic initial conditions in the good Boussinesq equation.

Findings

Existence of a unique local solution in a small time interval.

Solution has an expansion with exponentially decaying Fourier coefficients.

The time interval depends on initial data and frequency vector.

Abstract

This paper concerns the local well-posedness for the "good" Boussinesq equation subject to quasi-periodic initial conditions. By constructing a delicately and subtly iterative process together with an explicit combinatorial analysis, we show that there exists a unique solution for such a model in a small region of time. The size of this region depends on both the given data and the frequency vector involved. Moreover the local solution has an expansion with exponentially decaying Fourier coefficients.