Remarks on \(L^{2}\) decay of solutions for the third-grade non-Newtonian fluid flows in \(\mathbb{R}^{3}\). (English) Zbl 1379.35243
Summary: This paper is concerned with the improved \(L^{2}\) decay for solutions of a class of the third-grade non-Newtonian fluid flows in \(\mathbb {R}^{3}\). By developing the classic Fourier splitting methods, we prove the non-uniform decay of solutions when \(u_{0}\in L^{2}(\mathbb {R}^{3})\) and improve algebraic decay rates of solutions as \((1+t)^{{-\frac{3}{2}}({\frac{1}{r}}-{\frac{1}{2}})-\frac{1}{2}}\) when the initial data satisfy some moment condition. The results extend the previous result by C. Zhao et al. [Nonlinear Anal., Real World Appl. 15, 229–238 (2014; Zbl 1297.35194)].
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 76A05 | Non-Newtonian fluids |
| 76M25 | Other numerical methods (fluid mechanics) (MSC2010) |
Citations:
Zbl 1297.35194References:
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