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Further existence results for classical solutions of the equations of a second-grade fluid. (English) Zbl 0833.76005
A theoretical investigation is carried out on the equations of motion of an incompressible homogeneous fluid of the second grade. The question of existence and uniqueness of solution is revisited with the objective of removing a restriction on a material parameter \(\alpha =1/\rho \) imposed in previous works. By an appropriate splitting of the original problem along with the use of Schauder fixed point theorem, the authors show that if the domain \(\Omega\) is simply connected and the initial data not too large, the problem admits a unique classical solution, global in time, for any \(\alpha>0\).
This is an interesting result in the area of theoretical non-Newtonian fluid mechanics, and it is presented in a very well-written paper.

MSC:
76A05 Non-Newtonian fluids
35Q35 PDEs in connection with fluid mechanics
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