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On the regularity of weak solution for the Oberbeck-Boussinesq equations

Blanca Climent-Ezquerra, Elva Ortega-Torres, Marco Rojas-Medar

Abstract

We prove new regularity criteria of the Prodi-Serrin type with weak Lebesgue integrability in both space and time for a viscous active chemical fluid in a bounded domain.

On the regularity of weak solution for the Oberbeck-Boussinesq equations

Abstract

We prove new regularity criteria of the Prodi-Serrin type with weak Lebesgue integrability in both space and time for a viscous active chemical fluid in a bounded domain.
Paper Structure (8 sections, 4 theorems, 37 equations)

This paper contains 8 sections, 4 theorems, 37 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Notation
  4. Weak Lebesgue or Marcinkiewicz spaces
  5. Previous results
  6. The main results
  7. Proof of Theorem \ref{['Th.uno']}
  8. Proof of Theorem \ref{['Th.dos']}

Key Result

Lemma 2.1

If $f\in L^p(\Omega)$, then

Theorems & Definitions (5)

  • Lemma 2.1
  • Lemma 2.2
  • Theorem 3.1
  • Theorem 3.2
  • Remark 3.3