H\"{o}lder Continuous Periodic Solution of Boussinesq Equation with Partial Viscosity

TL;DR

This paper proves the existence of a H"older continuous periodic solution with compact support in time for the Boussinesq equations with partial viscosity, highlighting anisotropic regularity aligned with the viscosity properties.

Contribution

It introduces the first construction of anisotropic H"older continuous periodic solutions for Boussinesq equations with partial viscosity.

Findings

Existence of anisotropic H"older continuous periodic solutions.

Solutions have compact support in time.

Regularity aligns with partial viscosity characteristics.

Abstract

We show the existence of H\"older continuous periodic solution with compact support in time of the Boussinesq equations with partial viscosity. The H\"older regularity of the solution we constructed is anisotropic which is compatible with partial viscosity of the equations.