Global-in-time Hölder continuity of the velocity gradients for fluids with shear-dependent viscosities. (English) Zbl 0991.35066
For an evolutionary nonlinear fluid model characterized by the viscosity being a decreasing function of the modulus of the symmetric velocity gradient we establish global-in-time existence of the solution with Hölder continuous velocity gradients. Such a solution is unique in the class of weak solutions. We deal with the two dimensional space periodic problem.
MSC:
35Q35 | PDEs in connection with fluid mechanics |
35B65 | Smoothness and regularity of solutions to PDEs |
35K55 | Nonlinear parabolic equations |
76D03 | Existence, uniqueness, and regularity theory for incompressible viscous fluids |