Upper and lower bounds of time decay rate of solutions to a class of incompressible third grade fluid equations. (English) Zbl 1297.35194
Summary: This paper discusses the large time behaviors of solutions for a class of incompressible third grade fluid equations in \(\mathbb R^3\). Using the Fourier splitting method of M. Schonbek [in: Advances in geometric analysis and continuum mechanics. Proceedings of a conference, held at Stanford University, Stanford, CA, USA, 1993 in honor of the seventieth birthday of Robert Finn. Cambridge, MA: International Press. 269–274 (1995; Zbl 0842.35142)], the authors prove the upper and lower bounds of the time decay rate in \(\mathbb L^2\) for the weak solutions. The upper and lower bounds of decay rate are optimal in the sense that they coincide with the upper and lower bounds of the decay rate of solutions to the heat equation.
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 35Q79 | PDEs in connection with classical thermodynamics and heat transfer |
| 35D30 | Weak solutions to PDEs |
| 76A05 | Non-Newtonian fluids |
Citations:
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