On an inviscid model for incompressible two-phase flows with nonlocal interaction. (English) Zbl 1359.35128
Summary: We consider a diffuse interface model which describes the motion of an ideal incompressible mixture of two immiscible fluids with nonlocal interaction in two-dimensional bounded domains. This model consists of the Euler equation coupled with a convective nonlocal Cahn-Hilliard equation. We establish the existence of globally defined weak solutions as well as well-posedness results for strong/classical solutions.
MSC:
| 35Q30 | Navier-Stokes equations |
| 45K05 | Integro-partial differential equations |
| 37L30 | Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems |
| 76D03 | Existence, uniqueness, and regularity theory for incompressible viscous fluids |
| 76T99 | Multiphase and multicomponent flows |
Keywords:
incompressible binary fluids; Navier-Stokes equations; Euler equations; nonlocal Cahn-Hilliard equations; weak solutions; uniqueness; strong solutionsReferences:
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