an:06350862
Zbl 1300.35109
Ye, Zhuan
Blow-up criterion of smooth solutions for the Boussinesq equations
EN
Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 110, 97-103 (2014).
00336764
2014
j
35Q35 35B65 76D03 35B44 26A33 35R11
Boussinesq equations; fractional dissipation; blow-up criterion
Summary: This paper is dedicated to the study the Boussinesq equations with fractional dissipation in \(n\)-dimensions (\(n \geq 2\)). We obtain a blow-up criterion for the local in time classical solution to the Boussinesq equations with arbitrarily small fractional powers of the Laplacian. Therefore our results significantly improve the previous works and are more closer to the resolution of the well-known regularity criterion issue on the inviscid Boussinesq equations.