## Bilatu

25-tik 1-10 emaitza erakusten

#### Topological singular set of vector-valued maps, I: application to manifold-constrained Sobolev and BV spaces

(Calculus of Variations and Partial Differential Equations, 2019-03-30)

We introduce an operator $\mathbf{S}$ on vector-valued maps $u$ which has the ability to capture the relevant topological information carried by $u$.
In particular, this operator is defined on maps that take values in a ...

#### Order Reconstruction for neatics on squares with isotropic inclusions: A Landau-de Gennes study

(SIAM Journal on Applied Mathematics, 2019-03-30)

e study a modified Landau-de Gennes model for nematic liq- uid crystals, where the elastic term is assumed to be of subquadratic growth in the gradient. We analyze the behaviour of global minimizers in two- and three-dimensional ...

#### Convex Integration Arising in the Modelling of Shape-Memory Alloys: Some Remarks on Rigidity, Flexibility and Some Numerical Implementations

(Journal of Nonlinear Science, 2019-03-30)

We study convex integration solutions in the context of the modelling of shape-memory
alloys. The purpose of the article is twofold, treating both rigidity and flexibility prop-
erties: Firstly, we relate the maximal ...

#### The excluded volume of two-dimensional convex bodies: shape reconstruction and non-uniqueness

(Journal of Physics A: Mathematical and Theoretical, 2019-02-05)

In the Onsager model of one-component hard-particle systems, the entire phase behaviour is dictated by a function of relative orientation, which represents the amount of space excluded to one particle by another at this ...

#### A Global well-posedness result for the Rosensweig system of ferrofluids

(Rev. Mat. Iberoam., 2019)

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 ...

#### On the influence of gravity on density-dependent incompressible periodic fluids

(J. Differential Equations, 2019)

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 ...

#### Asymptotic models for free boundary flow in porous media

(Physica D, 2019)

We provide rigorous asymptotic models for the free boundary Darcy and Forchheimer problem under the assumption of weak nonlinear interaction, in a regime in which the steepness parameter of the interface is considered to ...

#### Some remark on the existence of infinitely many nonphysical solutions to the incompressible Navier-Stokes equations

(Journal of Mathematical Analysis and Applications, 2018-10)

We prove that there exist infinitely many distributional solutions with infinite kinetic energy to both the incompressible Navier-Stokes equations in $ \mathbb{R}^2 $ and Burgers equation in $\mathbb{R} $ with vanishing ...

#### On the global well-posedness of a class of 2D solutions for the Rosensweig system of ferrofluids

(Journal of Differential Equations, 2018-09)

We study a class of 2D solutions of a Bloch-Torrey regularization of the Rosensweig system in the whole space, which arise when the initial data and the external magnetic field are 2D. We prove that such solutions are ...

#### Uniqueness of degree-one Ginzburg–Landau vortex in the unit ball in dimensions N ≥ 7

(Comptes Rendus Mathematique, 2018-09-01)

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 ...