REMARKS ON THE BLOW-UP CRITERION FOR THE 3-D BOUSSINESQ EQUATIONS-Reference-Cited by-同舟云学术

REMARKS ON THE BLOW-UP CRITERION FOR THE 3-D BOUSSINESQ EQUATIONS

Published:1999-12 Issue:09 Volume:09 Page:1323-1332
ISSN:0218-2025
Container-title:Mathematical Models and Methods in Applied Sciences
language:en
Short-container-title:Math. Models Methods Appl. Sci.

Author:

ISHIMURA NAOYUKI¹,MORIMOTO HIROKO²

Affiliation:

1. Department of Mathematics, Hitotsubashi University, Kunitachi, Tokyo 186-8601, Japan

2. Department of Mathematics, School of Science and Technology, Meiji University, Tama-ku, Kawasaki 214-8571, Japan

Abstract

We consider the problem of blow-up of smooth solutions for the 3-D Boussinesq equations. Owing to the viscosity, we prove that the maximum norm of the gradient of vorticity controls the breakdown of the solutions; the scalar temperature function is shown to be irrelevant to the breakdown.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218202599000580

Reference20 articles.

1. Ladder theorems for the 2D and 3D Navier-Stokes equations on a finite periodic domain

2. Length scales in solutions of the Navier-Stokes equations

3. Remarks on the breakdown of smooth solutions for the 3-D Euler equations

4. Local existence and blow-up criterion for the Boussinesq equations

5. Note on loss of regularity for solutions of the 3?D incompressible euler and related equations

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