Related papers: Positive solutions of viscoelastic problems
In dimensions one to three, the fundamental solution to the free wave equation is positive. Therefore, there exists a simple positivity criterion for solutions. We use this to obtain large global solutions to two well-studied…
Viscoelastic materials have non-negative relaxation spectra. This property implies that viscoelastic response functions satisfy certain necessary and sufficient conditions. It is shown that these conditions can be expressed in terms of each…
We establish the local and global well-posedness of strong solutions to the two- and three-dimensional anelastic equations of stratified viscous flows. In this model, the interaction of the density profile with the velocity field is taken…
The Cauchy problem for a nonlinear elastic wave equations with viscoelastic damping terms is considered on the 3 dimensional whole space. Decay and smoothing properties of the solutions are investigated when the initial data are…
The wave equation with energy critical sources and nonlinear damping defined on a 3D bounded domain is considered. It is shown that the resulting dynamical system admits a global attractor. Under the additional assumption of strong…
The long-time regularity and asymptotic of weak solutions are studied for compressible Navier-Stokes equations with degenerate viscosity in a bounded periodic domain in two and three dimensions. It is shown that the density keeps strictly…
This paper concerns the Cauchy problem of the barotropic compressible Navier-Stokes equations on the whole two-dimensional space with vacuum as far field density. In particular, the initial density can have compact support. When the shear…
In this article, we consider the energy decay of a viscoelastic wave in an heterogeneous medium. To be more specific, the medium is composed of two different homogeneous medium with a memory term located in one of the medium. We prove…
A wavelike scalar-Einstein solution is found and indicating vectors constructed from the Bel-Robinson tensor are used to study which objects co-move with the wave and whether gravitational energy transfer is null.
We discuss a notion of weak solution for a semilinear wave equation that models the interaction of an elastic body with a rigid substrate through an adhesive layer, relying on results in [2]. Our analysis embraces the vector-valued case in…
We study the global decay properties of solutions to the linear wave equation in 1+3 dimensions on time-dependent, weakly asymptotically flat spacetimes. Assuming non-trapping of null geodesics and a local energy decay estimate, we prove…
We prove the existence of weak solutions to steady, compressible non-Newtonian Navier-Stokes system on a bounded, two- or three-dimensional domain. Assuming the viscous stress tensor is monotone satisfying a power-law growth with power $r$…
We describe how the kinematic consistency relations satisfied by density correlations of the large-scale structures of the Universe can be derived within the usual Newtonian framework. These relations express a kinematic effect and show how…
We consider a viscoelastic body occupying a smooth bounded domain of $R^3$ under the effects of volumic traction forces. Inertial effects are considered: hence, the equation describing the evolution of displacements is of the second order…
We introduce models for viscoelastic materials, both solids and fluids, based on logarithmic stresses to capture the elastic contribution to the material response. The matrix logarithm allows to link the measures of strain, that naturally…
The existence of scalar fields can be probed by observations of stochastic gravitational waves. Scalar fields mediate attractive forces, usually stronger than gravity, on the length scales shorter than their Compton wavelengths, which can…
We generalize the spacetime positive mass theorem to include multiple time dimensions. In particular, we show that the mass remains nonnegative in the sense that the energy $E$ is bounded from below by the trace norm of the linear momenta…
For periodic initial data with initial density allowed to vanish, we establish the global existence of strong and weak solutions for the two-dimensional compressible Navier-Stokes equations with no restrictions on the size of initial data…
In this article, we prove that solutions to a problem in nonlinear elasticity corresponding to small initial displacements exist globally in the exterior of a nontrapping obstacle. The medium is assumed to be homogeneous, isotropic, and…
An acoustic wave equation for pressure accounting for viscoelastic attenuation is derived from viscoelastic equations of motion. It is assumed that the relaxation moduli are completely monotonic. The acoustic equation differs significantly…