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- W2952259574 abstract "In our recent work dedicated to the Boussinesq equations [Danchin and Zhang 2016], we established the persistence of solutions with piecewise constant temperature along interfaces with Holder regularity. We here address the same problem for the inhomogeneous Navier-Stokes equations satisfied by a viscous incompressibleand inhomogeneous fluid. We establish that, indeed, in the slightly inhomogeneous case, patches of densities with $mathcal{C}^{1, varepsilon}$ regularity propagate for all time. As in [Danchin and Zhang 2016], our result follows from the conservation of Holder regularityalong vector fields moving with the flow. The proof of that latter result is based on commutator estimates involving para-vector fields, and multiplier spaces. The overall analysis is more complicated than in [Danchin and Zhang 2016] however, since the coupling between the mass and velocity equations in the inhomogeneous Navier-Stokes equations is emph{quasilinear} while it is linear for the Boussinesq equations." @default.
- W2952259574 created "2019-06-27" @default.
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- W2952259574 date "2016-12-01" @default.
- W2952259574 modified "2023-09-27" @default.
- W2952259574 title "On the persistence of Holder regular patches of density for the inhomogeneous Navier-Stokes equations" @default.
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