Related papers: On a hyperbolic system arising in liquid crystals …
This work is devoted to the study of dissipative fluid systems, through the lens of a geometric variational formulation. Building upon previous works extending Hamilton's principle to non-equilibrium thermodynamics, the present method…
We study the diffusive relaxation limit of the Jin-Xin system toward viscous conservation laws in the multi-dimensional setting. For initial data being small perturbations of a constant state in suitable homogeneous Besov norms, we prove…
The Equation Problem in finitely presented groups asks if there exists an algorithm which determines in finite amount of time whether any given equation system has a solution or not. We show that the Equation Problem in central extensions…
This paper concerns the global-in-time evolution of a generic compressible two-fluid model in $\mathbb{R}^d$ ($d\geq3$) with the common pressure law. Due to the non-dissipative properties for densities and two different particle paths…
In this paper we introduce the hyperbolic mean curvature flow and prove that the corresponding system of partial differential equations are strictly hyperbolic, and based on this, we show that this flow admits a unique short-time smooth…
We prove the global strong solvability of a quasilinear initial-boundary value problem with fractional time derivative of order less than one. Such problems arise in mathematical physics in the context of anomalous diffusion and the…
We illustrate and emphasize the relevance of hyperbolic theories of dissipation in different physical scenarios. Particular attention is paid to self-gravitating systems where the relaxation time may become large enough as to require a…
A statistical thermodynamic development is given of a new implicit solvent model that avoids the traditional system size limitations of computer simulation of macromolecular solutions with periodic boundary conditions. This implicit solvent…
Properties of an infinite system of nonlinearly coupled ordinary differential equations are discussed. This system models some properties present in the equations of motion for an inviscid fluid such as the skew symmetry and the…
Contrary to what is asserted in a recent paper by Kostadt and Liu ("Causality and stability of the relativistic diffusion equation"), experiments can tell apart (and in fact do) hyperbolic theories from parabolic theories of dissipation. It…
Analytical analysis of spatially extended autocatalytic and hypercyclic systems is presented. It is shown that spatially explicit systems in the form of reaction-diffusion equations with global regulation possess the same major qualitative…
Chaotic systems arise naturally in Statistical Mechanics and in Fluid Dynamics. A paradigm for their modelization are smooth hyperbolic systems. Are there consequences that can be drawn simply by assuming that a system is hyperbolic? here…
The paper studies the long time behavior of a system that describes the motion of a piece of elastic membrane driven by surface tension and inner air pressure. The system is a degenerate quasilinear hyperbolic one that involves the mean…
A classical 3-D thermoviscoelastic system of Kelvin-Voigt type is considered. The existence and uniqueness of a global regular solution is proved without small data assumption. The existence proof is based on the successive approximation…
We develop a dynamical systems theory for the compressible Navier-Stokes equations based on global in time weak solutions. The following questions will be addressed: Global existence and critical values of the adiabatic constant;…
Global existence for weak solutions to systems of nematic liquid crystals, with non-constant fluid density has been established by several authors. In this paper, we establish the regularity and uniqueness results for solutions to the…
Some future global properties of cosmological solutions for the Einstein-Vlasov-Maxwell system with surface symmetry are presented. Global existence is proved, the homogeneous spacetimes are future complete for causal trajectories, and the…
Ericksen and Leslie established a theory to model the flow of nematic liquid crystals. This paper is devoted to the Cauchy Problem of a simplified version of their system, which retains most of the properties of the original one. We…
Despite decades of intense study, the mechanisms underlying the extraordinary dynamics of supercooled liquids as they approach the glass transition remain, at best, mis-characterized, and at worst, misunderstood. A long standing endeavor is…
We study a simplified system of the original Ericksen--Leslie equations for the flow of nematic liquid crystals. This is a coupled non-parabolic dissipative dynamic system. We show the convergence of global classical solutions to single…