Well-posedness of weak solutions to electrorheological fluid equations with degeneracy on the boundary
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Date
2017-01-12
Authors
Zhan, Huashui
Wen, Jie
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In 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.
Description
Keywords
Electrorheological fluid equation, Boundary degeneracy, Holder's inequality, Local stability
Citation
Zhan, 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.
Rights
Attribution 4.0 International