Abstract.
We rigorously study the Navier-Stokes equation with a hereditary viscous term which depends on the past history. Such models arise in the dynamics of non-Newtonian fluids and also as viscoelastic models for the dynamics of turbulence statistics in Newtonian fluids. This problem is mathematically harder than the conventional Navier-Stokes problem due to the lack of certain global estimates. We prove the local solvability theorem using a suitable intermediate m-accretive quantization of the nonlinear term. Finite speed of propagation property of the vorticity field is also proved.
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Received: May 29, 2001
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Barbu, V., Sritharan, S. Navier-Stokes equation with hereditary viscosity. Z. angew. Math. Phys. 54, 449–461 (2003). https://doi.org/10.1007/s00033-003-1087-y
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DOI: https://doi.org/10.1007/s00033-003-1087-y