22 research outputs found
On 2D Viscoelasticity with Small Strain
An exact two-dimensional rotation-strain model describing the motion of
Hookean incompressible viscoelastic materials is constructed by the polar
decomposition of the deformation tensor. The global existence of classical
solutions is proved under the smallness assumptions only on the size of initial
strain tensor. The proof of global existence utilizes the weak dissipative
mechanism of motion, which is revealed by passing the partial dissipation to
the whole system.Comment: Different contributions of strain and rotation of the deformation are
studied for viscoelastic fluids of Oldroyd-B type in 2
Self-gravitating elastic bodies
Extended objects in GR are often modelled using distributional solutions of
the Einstein equations with point-like sources, or as the limit of
infinitesimally small "test" objects. In this note, I will consider models of
finite self-gravitating extended objects, which make it possible to give a
rigorous treatment of the initial value problem for (finite) extended objects.Comment: 16 pages. Based on a talk given at the 2013 WE-Heraeus seminar on
"Equations of motion in relativistic gravity
Global Solutions for Incompressible Viscoelastic Fluids
We prove the existence of both local and global smooth solutions to the
Cauchy problem in the whole space and the periodic problem in the n-dimensional
torus for the incompressible viscoelastic system of Oldroyd-B type in the case
of near equilibrium initial data. The results hold in both two and three
dimensional spaces. The results and methods presented in this paper are also
valid for a wide range of elastic complex fluids, such as magnetohydrodynamics,
liquid crystals and mixture problems.Comment: We prove the existence of global smooth solutions to the Cauchy
problem for the incompressible viscoelastic system of Oldroyd-B type in the
case of near equilibrium initial dat
The null condition and global existence of solutions to systems of wave equations with different speeds
In this paper, we consider the initial value problems to systems of quasilinear wave equations with different speeds in two space dimensions. Applying John-Shatah observations to our problem, we introduce the null condition for the system with different speeds. Moreover, we prove a global existence theorem for a class satisfying the null condition
NONLINEAR WAVES Proceedings of the Fourth MSJ International Research Institute Vol I
Sapporo, July 10-21, 199