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Regularity criterion for the incompressible viscoelastic fluid system. (English) Zbl 1230.76008

The authors study a system of equations modeling a neo-Hookean material. The constitutive equations are incorrectly referred to as the “Oldroyd-B model” (upper-convected Jeffreys fluid).
A regularity criterion for the velocity gradient is given in the three-dimensional case. A regularized version of the governing equations in two space dimensions is shown to permit global-in-time smooth solutions.

MSC:

76A05 Non-Newtonian fluids
35Q35 PDEs in connection with fluid mechanics
74D10 Nonlinear constitutive equations for materials with memory
35B65 Smoothness and regularity of solutions to PDEs
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