Strong solutions for two-dimensional nonlocal Cahn–Hilliard–Navier–Stokes systems

0394922 - MÚ 2014 RIV US eng J - Článek v odborném periodiku
Frigeri, S. - Grasselli, M. - Krejčí, Pavel
Strong solutions for two-dimensional nonlocal Cahn–Hilliard–Navier–Stokes systems.
Journal of Differential Equations. Roč. 255, č. 9 (2013), s. 2587-2614. ISSN 0022-0396. E-ISSN 1090-2732
Grant CEP: GA ČR GAP201/10/2315
Institucionální podpora: RVO:67985840
Klíčová slova: nonlocal Cahn-Hilliard equations * Navier-Stokes equations * global attractors
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 1.570, rok: 2013
http://www.sciencedirect.com/science/article/pii/S0022039613002830

A well-known diffuse interface model for incompressible isothermal mixtures of two immiscible fluids consists of the Navier-Stokes system coupled with a convective Cahn-Hilliard equation. In some recent contributions the standard Cahn-Hilliard equation has been replaced by its nonlocal version. The only known results are essentially the existence of a global weak solution and the existence of a suitable notion of global attractor for the corresponding dynamical system defined without uniqueness.In fact, even in the two-dimensional case, uniqueness of weak solutions is still an open problem. Here we take a step forward in the case of regular potentials. First we prove the existence of a (unique) strong solution in two dimensions. Then we show that any weak solution regularizes in finite time uniformly with respect to bounded sets of initial data. This result allows us to deduce that the global attractor is the union of all the bounded complete trajectories which are strong solutions.
Trvalý link: http://hdl.handle.net/11104/0223067