Applied Analysis
http://hdl.handle.net/20.500.11824/2
2019-02-23T09:12:30ZOn the influence of gravity on density-dependent incompressible periodic fluids
http://hdl.handle.net/20.500.11824/936
On the influence of gravity on density-dependent incompressible periodic fluids
Ngo V.-S.; Scrobogna S.
The present work is devoted to the analysis of density-dependent, incompressible fluids in a 3D torus, when the Froude number $\varepsilon$ goes to zero. We consider the very general case where the initial data do not have a zero horizontal average, where we only have smoothing effect on the velocity but not on the density and where we can have resonant phenomena on the domain. We explicitly determine the limit system when $\varepsilon \to 0$ and prove its global wellposedness. Finally, we prove that for large initial data, the density-dependent, incompressible fluid system is globally wellposed, provided that $\varepsilon$ is small enough.
2019-01-01T00:00:00ZA Global well-posedness result for the Rosensweig system of ferrofluids
http://hdl.handle.net/20.500.11824/916
A Global well-posedness result for the Rosensweig system of ferrofluids
Scrobogna S.; De Anna F.
In this Paper we study a Bloch-Torrey regularization of the Rosensweig system for ferrofluids. The scope of this paper is twofold. First of all, we investigate the existence and uniqueness of Leray-Hopf solutions of this model in the whole space $\mathbb{R}^2$.
In the second part of this paper we investigate both the long-time behavior of weak solutions and the propagation of Sobolev regularities in dimension two
2019-01-01T00:00:00ZUniqueness of degree-one Ginzburg–Landau vortex in the unit ball in dimensions N ≥ 7
http://hdl.handle.net/20.500.11824/868
Uniqueness of degree-one Ginzburg–Landau vortex in the unit ball in dimensions N ≥ 7
Ignat R.; Nguyen L.; Slastikov V.; Zarnescu A.
For ε>0, we consider the Ginzburg-Landau functional for RN-valued maps defined in the unit ball BN⊂RN with the vortex boundary data x on ∂BN. In dimensions N≥7, we prove that for every ε>0, there exists a unique global minimizer uε of this problem; moreover, uε is symmetric and of the form uε(x)=fε(|x|)x|x| for x∈BN.
2018-09-01T00:00:00ZShear flow dynamics in the Beris-Edwards model of nematic liquid crystals
http://hdl.handle.net/20.500.11824/867
Shear flow dynamics in the Beris-Edwards model of nematic liquid crystals
Murza A.C.; Teruel A.E.; Zarnescu A.
We consider the Beris-Edwards model describing nematic liquid crystal dynamics and restrict to a shear flow and spatially homogeneous situation. We analyze the dynamics focusing on the effect of the flow. We show that in the co-rotational case one has gradient dynamics, up to a periodic eigenframe rotation, while in the non-co-rotational case we identify the short and long time regime of the dynamics. We express these in terms of the physical variables and compare with the predictions of other models of liquid crystal dynamics.
2018-02-14T00:00:00Z