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Title of Journal: Calc Var

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Abbravation: Calculus of Variations and Partial Differential Equations

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Springer Berlin Heidelberg

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DOI

10.1007/978-981-10-0875-7_7

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ISSN

1432-0835

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Cahn–Hilliard–Navier–Stokes systems with moving co

Authors: C G Gal M Grasselli A Miranville
Publish Date: 2016/05/11
Volume: 55, Issue: 3, Pages: 50-
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Abstract

We consider a wellknown diffuse interface model for the study of the evolution of an incompressible binary fluid flow in a two or threedimensional bounded domain This model consists of a system of two evolution equations namely the incompressible NavierStokes equations for the average fluid velocity u coupled with a convective Cahn–Hilliard equation for an order parameter phi The novelty is that the system is endowed with boundary conditions which account for a moving contact line slip velocity The existence of a suitable global energy solution is proven and the convergence of any such solution to a single equilibrium is also establishedM Grasselli is a member of the Gruppo Nazionale per l’Analisi Matematica la Probabilità e le loro Applicazioni GNAMPA of the Istituto Nazionale di Alta Matematica INdAM We also wish to acknowledge the reviewer whose comments and important remarks have improved the initial version of the article We thank Hao Wu for pointing out a gap in a previous proof of Theorem 33

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  2. Fractional Poincaré inequality with finite total Q -curvature
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  4. Thick clusters for the radially symmetric nonlinear Schrödinger equation
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  7. Duality for rectified cost functions
  8. An approach to minimization under a constraint: the added mass technique
  9. Single-point condensation phenomena for a four-dimensional biharmonic Ren–Wei problem
  10. Uniqueness and nondegeneracy of positive radial solutions of $$\mathbf {div\,{\varvec{(}}{\varvec{\rho }} \nabla u{\varvec{)}} +{\varvec{\rho }}{\varvec{(}}-gu+hu^p{\varvec{)}}=0}$$
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  12. Lower bounds of Dirichlet eigenvalues for some degenerate elliptic operators
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  14. On Newton equations which are totally integrable at infinity
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  16. Regularity for fully nonlinear nonlocal parabolic equations with rough kernels
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  18. Weak KAM theory for a weakly coupled system of Hamilton–Jacobi equations
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