On Nonsymmetric Two-Dimensional Viscous Flow Through an Aperture

L.P. Rivkind and V.A. Solonnikov

Abstract: We consider a stationary free boundary problem for the Navier-Stokes equations governing effluence of a viscous incompressible liquid out of unbounded non-expanding at infinity, in general, non-symmetric strip-like domain $\Omega_-$ outside which the liquid forms a sector-like 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 cross-section 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.

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