Higher order regularity and blow-up criterion for semi-dissipative and ideal Boussinesq equations
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In: Journal of mathematical physics, Vol. 60.2018, No. 4, 041503, 15.04.2019.
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TY - JOUR
T1 - Higher order regularity and blow-up criterion for semi-dissipative and ideal Boussinesq equations
AU - Manna, Utpal
AU - Panda, Akash
N1 - Publisher Copyright: © 2019 Author(s).
PY - 2019/4/15
Y1 - 2019/4/15
N2 - In this paper, we establish local-in-time existence and uniqueness of strong solutions in Hs for s>n2 to the viscous, zero thermal-diffusive Boussinesq equations in Rn,n=2,3. Beale-Kato-Majda type blow-up criterion has been established in three dimensions with respect to the BMO-norm of the vorticity. We further prove the local-in-time existence for nonviscous and fully ideal Boussinesq systems in Rn,n=2,3. Moreover, we establish blow-up criterion for nonviscous Boussinesq system in three dimensions and for fully ideal Boussinesq system in both two and three dimensions. Commutator estimates from the work of Kato and Ponce [Comm. Pure Appl. Math. 41, 891 (1988)] and Fefferman et al. [J. Funct. Anal. 267, 1035 (2014)] play important roles in the calculations.
AB - In this paper, we establish local-in-time existence and uniqueness of strong solutions in Hs for s>n2 to the viscous, zero thermal-diffusive Boussinesq equations in Rn,n=2,3. Beale-Kato-Majda type blow-up criterion has been established in three dimensions with respect to the BMO-norm of the vorticity. We further prove the local-in-time existence for nonviscous and fully ideal Boussinesq systems in Rn,n=2,3. Moreover, we establish blow-up criterion for nonviscous Boussinesq system in three dimensions and for fully ideal Boussinesq system in both two and three dimensions. Commutator estimates from the work of Kato and Ponce [Comm. Pure Appl. Math. 41, 891 (1988)] and Fefferman et al. [J. Funct. Anal. 267, 1035 (2014)] play important roles in the calculations.
UR - http://www.scopus.com/inward/record.url?scp=85064478135&partnerID=8YFLogxK
U2 - 10.1063/1.5048839
DO - 10.1063/1.5048839
M3 - Article
VL - 60.2018
JO - Journal of mathematical physics
JF - Journal of mathematical physics
SN - 0022-2488
IS - 4
M1 - 041503
ER -
