PORTUGALIAE MATHEMATICA Vol. 57, No. 4, pp. 381414 (2000) 

On Nonsymmetric TwoDimensional Viscous Flow Through an ApertureL.P. Rivkind and V.A. SolonnikovDepartment of Mathematics, University of Dortmund  GERMANYEmail: rivkind@math.unidortmund.de V.A. Steklov Math. Inst., S. Petersburg  RUSSIA Email: solonnik@pdmi.ras.ru , slk@dns.unife.it Abstract: We consider a stationary free boundary problem for the NavierStokes equations governing effluence of a viscous incompressible liquid out of unbounded nonexpanding at infinity, in general, nonsymmetric striplike domain $\Omega_$ outside which the liquid forms a sectorlike jet with free (unknown) boundary and with the limiting opening angle $\theta\in(0,\pi/2)$. Conditions at the free boundary take account of the capillary forces but external forces are absent. The total flux of the liquid through arbitrary crosssection of $\Omega_$ is prescribed and assumed to be small. Under this condition, we prove the existence of an isolated solution of the problem which is found in a certain weighted Hölder space of functions. Full text of the article:
Electronic version published on: 31 Jan 2003. This page was last modified: 27 Nov 2007.
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