Generalized Beltrami flows and other closed-form solutions of an unsteady viscoelastic fluid.
Generalized Fluid Flows, Their Approximation and Applications.
Generalized lubrification models blow-up and global existence result.
We study a general mathematical model linked with various physical models. Especially, we focus on those models established by King or Spencer-Davis-Voorhees related to thin films extending the lubrication model studied by Bernis-Friedman. According to the initial data, we prove that, either, blow up or global existence can be obtained.
Geometrodynamics of some non-relativistic incompressible fluids.
In some previous papers [1, 2] we proposed a geometric formulation of continuum mechanics, where a continuous body is seen as a suitable differentiable fiber bundle C on the Galilean space-time M, beside a differential equation of order k, Ek(C), on C and the assignement of a frame Psi on M. This approach allowed us to treat continuum mechanics as a unitary field theory and to consider constitutive and dynamical properties in a more natural way. Further, the particular intrinsic geometrical framework...
Global Attractor for a Fourth-Order Parabolic Equation Modeling Epitaxial Thin Film Growth
This paper is concerned with a fourth-order parabolic equation which models epitaxial growth of nanoscale thin films. Based on the regularity estimates for semigroups and the classical existence theorem of global attractors, we prove that the fourth order parabolic equation possesses a global attractor in a subspace of H², which attracts all the bounded sets of H² in the H²-norm.
Global existence and one-dimensional nonlinear stability of shearing motions of viscoelastic fluids of Oldroyd type
Global existence of strong solutions to the one-dimensional full model for phase transitions in thermoviscoelastic materials
This paper is devoted to the analysis of a one-dimensional model for phase transition phenomena in thermoviscoelastic materials. The corresponding parabolic-hyperbolic PDE system features a strongly nonlinear internal energy balance equation, governing the evolution of the absolute temperature , an evolution equation for the phase change parameter , including constraints on the phase variable, and a hyperbolic stress-strain relation for the displacement variable . The main novelty of the model...
Global mild solutions of the micropolar fluid system in critical spaces
We prove the global in time existence of a small solution for the 3D micropolar fluid system in critical Fourier-Herz spaces by using the Fourier localization method and Littlewood-Paley theory.
Global superconvergence approximations of the mixed finite element method for the Stokes problem and the linear elasticity equation