Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the General Ericksen-Leslie System: Parodi's Relation, Well-posedness
  and Stability   In this paper we investigate the role of Parodi's relation in the
well-posedness and stability of the general Ericksen-Leslie system modeling
nematic liquid crystal flows. First, we give a formal physical derivation of
the Ericksen-Leslie system through an appropriate energy variational approach
under Parodi's relation, in which we can distinguish the
conservative/dissipative parts of the induced elastic stress. Next, we prove
global well-posedness and long-time behavior of the Ericksen-Leslie system
under the assumption that the viscosity $\mu_4$ is sufficiently large. Finally,
under Parodi's relation, we show the global well-posedness and Lyapunov
stability for the Ericksen-Leslie system near local energy minimizers. The
connection between Parodi's relation and linear stability of the
Ericksen-Leslie system is also discussed.

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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: cs
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex