Author:
Choudhuri Debajyoti,Repovš Dušan D.
Abstract
AbstractWe establish the existence of at least two solutions of the Prandtl–Batchelor like elliptic problem driven by a power nonlinearity and a singular term. The associated energy functional is nondifferentiable, and hence the usual variational techniques do not work. We shall use a novel approach in tackling the associated energy functional by a sequence of $C^{1}$
C
1
functionals and a cutoff function. Our main tools are fundamental elliptic regularity theory and the mountain pass theorem.
Funder
National Board for Higher Mathematics
Slovenian Research Agency grants
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory,Analysis
Reference20 articles.
1. Acker, A.: On the existence of convex classical solutions to a generalized Prandtl-Batchelor free boundary problem. Z. Angew. Math. Phys. 49(1), 1–30 (1998)
2. Alt, H.W., Caffarelli, L.A.: Existence and regularity for a minimum problem with free boundary. J. Reine Angew. Math. 325, 105–144 (1981)
3. Ambrosetti, A., Rabinowitz, P.H.: Dual variational methods in critical point theory and applications. J. Funct. Anal. 14, 349–381 (1973)
4. Batchelor, G.K.: On steady state laminar flow with closed streamlines at large Reynolds number. J. Fluid Mech. 1, 177–190 (1956)
5. Batchelor, G.K.: A proposal concerning laminar wakes behind bluff bodies at large Reynolds number. J. Fluid Mech. 1, 388–398 (1956)
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献