Geodesic
Blow-up criterion for the zero-diffusive Boussinesq equations via the velocity components
Electronic Journal of Differential Equations, Tome 2015 (2015).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: This article concerns the blow up for the smooth solutions of the three-dimensional Boussinesq equations with zero diffusivity. It is shown that if any two components of the velocity field u satisfy $$ \int_0^T \frac{ \||u_1|+|u_2|\|^q_{L^{p,\infty}} } {1+\ln ( e+\|\nabla u\|^2_{L^2}) } ds\infty,\quad \frac{2}{q}+\frac{3}{p}=1,\quad 3\infty, $$ then the local smooth solution $(u,\theta)$ can be continuously extended to $(0,T_1)$ for some $T_1>T$.
Classification : 35Q35, 76D05
Keywords: zero-diffusive Boussinesq equations, blow up criterion, Lorentz spaces 
@article{EJDE_2015__2015__a24,
     author = {Wang, Weihua},
     title = {Blow-up criterion for the zero-diffusive {Boussinesq} equations via the velocity components},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2015},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a24/}
}
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Wang, Weihua. Blow-up criterion for the zero-diffusive Boussinesq equations via the velocity components. Electronic Journal of Differential Equations, Tome 2015 (2015). http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a24/