Local existence and blow-up criterion for the Boussinesq equations

Proceedings of the Royal Society of Edinburgh Section A: Mathematics - Tập 127 Số 5 - Trang 935-946 - 1997
Dongho Chae1, Hee-Seok Nam1
1Department of Mathematics, Seoul National University, Seoul, 151–742, Korea

Tóm tắt

SynopsisIn this paper, we prove local existence and uniqueness of smooth solutions of the Boussinesq equations. We also obtain a blow-up criterion for these smooth solutions. This shows that the maximum norm of the gradient of the passive scalar controls the breakdown of smooth solutions of the Boussinesq equations. As an application of this criterion, we prove global existence of smooth solutions in the case of zero external force.

Từ khóa


Tài liệu tham khảo

Majda, 1986, Vorticity and the mathematical theory of incompressible fluid flow, 10.1002/cpa.3160390711

Ohkitani, 1997, Some mathematical aspects of 2D vortex dynamics. Proc. Miniconference of Partial Differential Equations and Applications, RIM-GARC Lecture Note Ser., 38, 35

10.1007/BF01212349

10.1002/cpa.3160410704

Weinan, 1994, Small-scale structures in Boussinesq convection, Phys. Fluids, 6, 49, 10.1063/1.868044

Thông tin
Thông tin xuất bản

Proceedings of the Royal Society of Edinburgh Section A: Mathematics

Tập 127 Số 5

935-946

Thông tin tác giả