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arXiv · 2006.14502

Liouville theorems for a stationary and non-stationary coupled system of liquid crystal flows in local Morrey spaces

Oscar Jarrin
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Abstract

We consider here the simplified Ericksen-Leslie system on the whole three-dimensional space. This system deals with the incompressible Navier-Stokes equations strongly coupled with a harmonic map flow which models the dynamical behavior for nematic liquid crystals. For both the stationary (time independing) case and the non-stationary (time depending) case, using the fairly general framework of a kind of local Morrey spaces, we obtain some a priori conditions on the unknowns of this coupled system to prove that they vanish identically. This results are known as Liouville-type theorems. As a bi-product, our theorems also improve some well-known results on Liouville-type theorems for the particular case of classical Navier-Stokes equations

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Oscar Jarrin. 2021-07-20. Liouville theorems for a stationary and non-stationary coupled system of liquid crystal flows in local Morrey spaces. https://arxiv.org/abs/2006.14502

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