Existence of one class of global strong solution to the Cauchy problem for the three-dimensional incompressible Boussinesq system

TL;DR

This paper proves the global existence of strong solutions for a specific class of initial data in the 3D incompressible Boussinesq system, with solutions representable via Fourier series.

Contribution

It establishes the existence of a class of global strong solutions for the 3D Boussinesq system with special initial data, expanding understanding of solution behavior.

Findings

Existence of global strong solutions for special initial data.

Solutions can be expressed as Fourier series.

Advances understanding of the Boussinesq system's solution space.

Abstract

In this paper, we prove the the global existence of strong solutions to the three dimensional incompressible Boussinesq system with some special solenoidal initial data. In particular, these solutions can be expressed into the Fourier series.