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Now showing items 1-7 of 7

#### Sphere-valued harmonic maps with surface energy and the K13 problem

(Advances in the Calculus of Variations, 2017-11)

We consider an energy functional motivated by the celebrated K13 problem in the Oseen-Frank theory of nematic liquid crystals. It is defined for sphere-valued functions and appears as the usual Dirichlet energy with an ...

#### On a hyperbolic system arising in liquid crystal modelling

(Journal of Hyperbolic Differential Equations, 2017-11)

We consider a model of liquid crystals, based on a nonlinear hyperbolic system of
differential equations, that represents an inviscid version of the model proposed by Qian
and Sheng. A new concept of dissipative solution ...

#### Global well-posedness and twist-wave solutions for the inertial Qian-Sheng model of liquid crystals

(Journal of Differential Equations, 2017-10-02)

We consider the inertial Qian-Sheng model of liquid crystals which couples a hyperbolic-type equation involving a second-order material derivative with a forced incompressible Navier-Stokes system. We study the energy law ...

#### Dispersive effects of weakly compressible and fast rotating inviscid fluids

(Discrete and Continuous Dynamical Systems - Series A, 2017-08)

We consider a system describing the motion of an isentropic, inviscid, weakly compressible, fast rotating fluid in the whole space $\mathbb{R}^3$, with initial data belonging to $ H^s \left( \mathbb{R}^3 \right), s>5/2 $. ...

#### Derivation of limit equation for a singular perturbation of a 3D periodic Boussinesq system

(Discrete and Continuous Dynamical Systems - Series A, 2017-07-15)

We consider a system describing the dynamics of an hydrodynamical, density-dependent flow under the effects of gravitational forces. We prove that if the Froude number is sufficiently small such system is globally well ...

#### Highly rotating fluids with vertical stratification for periodic data and vanishing vertical viscosity

(Revista Matemática Iberoamericana, 2017-07)

We prove that the three-dimensional, periodic primitive equations with zero vertical diffusivity are globally well posed if the Rossby and Froude number are sufficiently small. The initial data is considered to be of zero ...

#### Partial regularity and smooth topology-preserving approximations of rough domains

(Calculus of Variations and Partial Differential Equations, 2017-01-01)

For a bounded domain $\Omega\subset\mathbb{R}^m, m\geq 2,$ of class $C^0$, the properties are studied of fields of `good directions', that is the directions with respect to which $\partial\Omega$ can be locally represented ...