Contents Online
Dynamics of Partial Differential Equations
Volume 15 (2018)
Number 3
Degenerate non-Newtonian fluid equation on the half space
Pages: 215 – 233
DOI: https://dx.doi.org/10.4310/DPDE.2018.v15.n3.a4
Authors
Abstract
The degenerate non-Newtonian fluid equation\[\frac{\partial u}{ \partial t} - \mathrm{div} (a(x) {\lvert \nabla u \rvert}^{p-2} \nabla u)- \sum^{N}_{i=1} f_i (x) D_i u = g(u, x, t), (x, t) \in \mathbb{R}^N_{+} \times (0, T)\]arises in several scientific fields. When $a(x)$ and $p$ satisfy certain conditions, the existence of solution of this equation is established. When $a^{-\frac{1}{p}} (x) f_i (x) \leq c$ for $i \in \lbrace 1, 2, \dotsm , N \rbrace$, by choosing a suitable test function, the local stability of the solutions is discussed without any boundary value condition.
Keywords
non-Newtonian fluid equation, half space, boundary value condition, local stability
2010 Mathematics Subject Classification
Primary 35B35, 35K55. Secondary 76A05.
This work is supported by National Science Foundation of Fujian Province under No. 2015J01592 and Natural Science Foundation of Xiamen University of Technology. It is also partially supported by UTRGV Faculty Research Council Award 110000327.
Received 28 May 2017
Published 29 May 2018