A note on the blow-up criterion for the inviscid 2-D Boussinesq equations. (English) Zbl 0991.35070
Salvi, Rodolfo (ed.), The Navier-Stokes equations: theory and numerical methods. Proceedings of the international conference, Varenna, Lecco, Italy, 2000. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 223, 131-140 (2002).
Summary: We show that a smooth solution of the 2-D Boussinesq equations
in the whole plane breaks down if and only if a certain norm of blows up at the same time. Here the norm is weaker than the -norm and generates a Banach space including singularities of . Roughly speaking, when a smooth solution breaks down, has stronger singularities than or has an infinite number of singularities.
|35Q35||PDEs in connection with fluid mechanics|
|35B40||Asymptotic behavior of solutions of PDE|
|76B07||Free-surface potential flows|