We consider entire solutions u of the equations describing the stationary flow of a generalized Newtonian fluid in 2D concentrating on the question,if a Liouville-type result holds in the sense that the boundedness of u implies its constancy.A positive answer is true for p-fluids in the case p ＞ 1 (including the classical Navier-Stokes system for the choice p =2),and recently we established this Liouville property for the Prandtl-Eyring fluid model,for which the dissipative potential has nearly linear growth.Here we finally discuss the case of perfectly plastic fluids whose flow is governed by a von Mises-type stress-strain relation formally corresponding to the case p =1.It turns out that,for dissipative potentials of linear growth,the condition of μ-ellipticity with exponent μ ＜ 2 is sufficient for proving the Liouville theorem.
展开▼
