Journal
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
Volume 55, Issue 5, Pages -Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00526-016-1051-2
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Funding
- Centre International de Rencontres Mathematiques
- Institut Henri Poincare
- Centro di Ricerca Matematica Ennio De Giorgi
- ANR [ANR-14-CE25-0009-01]
- EPSRC [EP/K02390X/1]
- Leverhulme Research Grant [RPG-2014-226]
- Romanian National Authority for Scientific Research and Innovation, CNCS-UEFISCDI [PN-II-RU-TE-2014-4-0657]
- EPSRC [EP/I028714/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/I028714/1] Funding Source: researchfish
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We study k-radially symmetric solutions corresponding to topological defects of charge k/2 for integer k not equal 0 in the Landau-de Gennes model describing liquid crystals in two-dimensional domains. We show that the solutions whose radial profiles satisfy a natural sign invariance are stable when vertical bar k vertical bar = 1 (unlike the case vertical bar k vertical bar > 1 which we treated before). The proof crucially uses the monotonicity of the suitable components, obtained by making use of the cooperative character of the system. A uniqueness result for the radial profiles is also established.
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