In this paper, we consider the two-dimensional Newton-Boussinesq equations with the incompressibility condition. We obtain a regularity criterion for the Newton-Boussinesq equations by virtue of the commutator estimate.
A note on regularity criterion for the 3D Boussinesq system with partial viscosity
β Scribed by Jishan Fan; Yong Zhou
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 298 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0893-9659
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
In this note we establish a Serrin-type regularity criterion in terms of pressure for Leray weak solutions to the Navier-Stokes equation in R d . Here we call u a Leray weak solution if u is a weak solution of finite energy, i.e. It is known that if a Leray weak solution u belongs to then u is reg
wh'ere the critical temperature Tc has been introduced. Equation (3) leads to a positive value of vm,n only when 27 r< Tc. In this case there exists a smallest value of w 2 on an isotherm. For T= Te we get, from equation ( 3), vm,n > vc. That leads to pm,n <p~, contrary to the expectation of Mannhe