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Boundary regularity of flows under perfect slip boundary conditions

Petr Kaplický; Jakub Tichý — 2013

Open Mathematics

We investigate boundary regularity of solutions of generalized Stokes equations. The problem is complemented with perfect slip boundary conditions and we assume that the nonlinear elliptic operator satisfies non-standard ϕ-growth conditions. We show the existence of second derivatives of velocity and their optimal regularity.

Full regularity of weak solutions to a class of nonlinear fluids in two dimensions -- stationary, periodic problem

Petr Kaplický; Josef Málek; Jana Stará — 1997

Commentationes Mathematicae Universitatis Carolinae

We prove the existence of regular solution to a system of nonlinear equations describing the steady motions of a certain class of non-Newtonian fluids in two dimensions. The equations are completed by requirement that all functions are periodic.

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