Related papers: Regularity of Minimizers of a Tensor-valued Variat…
We consider a four-elastic-constant Landau-de Gennes energy characterizing nematic liquid crystal configurations described using the $Q$-tensor formalism. The energy contains a cubic term and is unbounded from below. We study dynamical…
We investigate the properties of $Q$-balls in $d$ spatial dimensions. First, a generalized virial relation for these objects is obtained. We then focus on potentials $V(\phi\phi^{\dagger})= \sum_{n=1}^{3} a_n(\phi\phi^{\dagger})^n$, where…
Regularity results for minimal configurations of variational problems involving both bulk and surface energies and subject to a volume constraint are established. The bulk energies are convex functions with p-power growth, but are otherwise…
We address static and dynamical properties of one-dimensional (1D) quantum droplets (QDs) under the action of local potentials in the form of narrow wells and barriers. The QDs are governed by the 1D Gross-Pitaevskii equation including the…
In this paper we prove the existence of global in time weak solutions for an evolutionary PDE system modelling nonisothermal Landau-de Gennes nematic liquid crystal (LC) flows in three dimensions of space. In our model, the incompressible…
In this note, we investigate partial regularity of weak solutions of the three dimensional chemotaxis-Navier-Stokes equations, and obtain the $\frac53$-dimensional Hausdorff measure of the possible singular set is vanishing at the first…
We investigate prototypical profiles of point defects in two dimensional liquid crystals within the framework of Landau-de Gennes theory. Using boundary conditions characteristic of defects of index $k/2$, we find a critical point of the…
In this paper we investigate the vacuum expectation values of energy- momentum tensor for conformally coupled scalar field in the standard parallel plate geometry with Dirichlet boundary conditions and on background of planar domain wall…
In this paper, we consider the problem of minimizing quantum free energies under the constraint that the density of particles is fixed at each point of Rd, for any d $\ge$ 1. We are more particularly interested in the characterization of…
We study a geometric variational problem arising from modeling two-dimensional charged drops of a perfectly conducting liquid in the presence of an external potential. We characterize the semicontinuous envelope of the energy in terms of a…
The repulsion strength at the origin for repulsive/attractive potentials determines the regularity of local minimizers of the interaction energy. In this paper, we show that if this repulsion is like Newtonian or more singular than…
The blow-up in finite time for the solutions to the initial-boundary value problem associated to the multi-dimensional quantum hydrodynamic model in a bounded domain is proved. The model consists on conservation of mass equation and a…
We consider a thin film limit of a Landau-de Gennes Q-tensor model. In the limiting process we observe a continuous transition where the normal and tangential parts of the Q-tensor decouple and various intrinsic and extrinsic contributions…
We give a brief introduction to a divergence penalized Landau-de Gennes functional as a toy model for the study of nematic liquid crystal with colloid inclusion, in the case of unequal elastic constants. We assume that the nematic occupies…
We study global minimizers of the Landau-de Gennes (LdG) energy functional for nematic liquid crystals, on arbitrary three-dimensional simply connected geometries with topologically non-trivial and physically relevant Dirichlet boundary…
We study interior $\varepsilon$-regularity and Type I blowup criteria for suitable weak solutions to the three-dimensional incompressible MHD equations. Our starting point is a direct iteration scheme for the classical…
In this paper, we consider a resolvent problem arising from the $Q$-tensor model for liquid crystal flows in the half-space. Our purpose is to show the $\mathcal{R}$-boundedness for the solution operator families of the resolvent problem…
We report on a revision of our previous computation of the renormalized expectation value of the stress-energy tensor of a massless, minimally coupled scalar with a quartic self-interaction on a locally de Sitter background. This model is…
Onsager's conjecture states that the conservation of energy may fail for $3D$ incompressible Euler flows with H\"{o}lder regularity below $1/3$. This conjecture was recently solved by the author, yet the endpoint case remains an interesting…
We study a class of Landau-de Gennes energy functionals with a sextic bulk energy density in a three-dimensional domain. We examine the asymptotic behavior of uniformly bounded minimizers in two distinct scenarios: one where their energy…