Higher order regularity and blow-up criterion for semi-dissipative and ideal Boussinesq equations
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Authors
External Organisational units
- Indian Institute of Science Education and Research (IISER) Thiruvananthapuram
Abstract
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.
Details
Original language | English |
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Article number | 041503 |
Journal | Journal of mathematical physics |
Volume | 60.2018 |
Issue number | 4 |
DOIs | |
Publication status | E-pub ahead of print - 15 Apr 2019 |
Externally published | Yes |