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Existence and regularity for stationary incompressible flows with dissipative potentials of linear growth. (English) Zbl 1404.76011
Summary: We consider the slow flow of an incompressible fluid assuming in addition that the flow is also stationary. Our main assumption concerns the dissipative potential which is of linear growth with respect to the symmetric gradient of the velocity field. Thus our model can be seen as an approximation of the perfectly plastic case introduced by von Mises, and we will establish various results on existence and regularity of a solution.
MSC:
76A05 Non-Newtonian fluids
76M30 Variational methods applied to problems in fluid mechanics
49Q20 Variational problems in a geometric measure-theoretic setting
49N60 Regularity of solutions in optimal control
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