| Abstract: |
| In this talk, we discuss the well-posedness of the variational inequality for a fluid dynamics
of Bingham and Navier--Stokes type in three dimension.
This kind of problem was treated by Naumann--Wulst (1979), Kato (1993) for the Bingham fluid,
based on the result by Duvaut--Lions (1976).
All of them, the solution makes weak sense in $H^1$, because one could not get the enough $H^2$-regularity.
The problem is formulated the evolution equation governed by the subdifferential.
By discussing the characterization of the subdifferential, more precisely, the $H^2$-regularity result of the solution for the variational inequality, the Barbu truncation method works well to prove the well-posedness.
This talk is based on the joint work with Takahito Kashiwabara, The University of Tokyo. |
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