Exponential stability of an incompressible non-Newtonian fluid with delay. (English) Zbl 1418.76010
Summary: The existence and uniqueness of stationary solutions to an incompressible non-Newtonian fluid are first established. The exponential stability of steady-state solutions is then analyzed by means of four different approaches. The first is the classical Lyapunov function method, while the second one is based on a Razumikhin type argument. Then, a method relying on the construction of Lyapunov functionals and another one using a Gronwall-like lemma are also exploited to study the stability, respectively. Some comments concerning several open research directions about this model are also included.
MSC:
| 76A05 | Non-Newtonian fluids |
| 35B35 | Stability in context of PDEs |
| 35Q35 | PDEs in connection with fluid mechanics |
| 37L15 | Stability problems for infinite-dimensional dissipative dynamical systems |
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