Global existence of solutions of the liquid crystal flow for the Oseen-Frank model in \(\mathbb R^2\). (English) Zbl 1260.35113
The authors consider two problems. First, they show global in time existence of a weak solution to the liquid crystal flow for the Oseen-Frank model. The solution is actually smooth except for finite number of singularities in time-space.
In the second part they consider the Ericksen-Leslie system, i.e. a system of partial differential equations where the Navier-Stokes equations are coupled with the liquid crystal flow. For a general Oseen-Frank model (in two dimensions) they construct global in time weak solutions which are smooth except for a finite number of time instants. For both problems it is shown that the singularities can be characterized by the energy concentration around these points.
In the second part they consider the Ericksen-Leslie system, i.e. a system of partial differential equations where the Navier-Stokes equations are coupled with the liquid crystal flow. For a general Oseen-Frank model (in two dimensions) they construct global in time weak solutions which are smooth except for a finite number of time instants. For both problems it is shown that the singularities can be characterized by the energy concentration around these points.
Reviewer: Milan Pokorný (Praha)
MSC:
| 35Q30 | Navier-Stokes equations |
| 76A15 | Liquid crystals |
| 35D30 | Weak solutions to PDEs |
| 76D07 | Stokes and related (Oseen, etc.) flows |
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