On a variational inequality of Bingham and Navier–Stokes type

Takeshi Fukao (Kyoto University of Education)

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 H1, because one could not get the enough H2- regularity. The problem is formulated the evolution equation governed by the subdifferential. By discussing the characterization of the subdifferential, more precisely, the H2-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.