Zhan, HuashuiWen, Jie2022-03-162022-03-162017-01-12Zhan, H., & Wen, J. (2017). Well-posedness of weak solutions to electrorheological fluid equations with degeneracy on the boundary. <i>Electronic Journal of Differential Equations, 2017</i>(13), pp. 1-15.1072-6691https://hdl.handle.net/10877/15518In this article we study the electrorheological fluid equation ut = div(ρα|∇u|p(x)-2∇u), where ρ(x) = dist(x, ∂Ω) is the distance from the boundary, p(x) ∈ C1(Ω̅), and p¯ = min x∈Ω̅p(x) > 1. We show how the degeneracy of ρα on the boundary affects the well-posedness of the weak solutions. In particular, the local stability of the weak solutions is established without any boundary value condition.Text15 pages1 file (.pdf)enAttribution 4.0 InternationalElectrorheological fluid equationBoundary degeneracyHolder's inequalityLocal stabilityArticle