Related papers: Influence of the second viscosity on the flow prop…
Viscous flow of interacting electrons in two dimensional materials features a bunch of exotic effects. A model resembling the Navier-Stokes equation for classical fluids accounts for them in the so called hydrodynamic regime. We performed a…
In the first part, the stability of two-dimensional parallel flow is discussed. A more restrictively general stability criterion for inviscid parallel flow is obtained analytically. In the second part, we report the numerical simulations of…
We show that the system entropy change for the transitions between non-equilibrium steady states arbitrarily far from equilibrium for any constituting process is given by the relative entropy of the distributions of these steady states.…
We study average flow properties in porous media using a two-dimensional network simulator. It models the dynamics of two-phase immiscible bulk flow where film flow can be neglected. The boundary conditions are biperiodic which provide a…
We study the nonlinear stability of plane Couette and Poiseuille flows with the Lyapunov second method by using the classical L2-energy. We prove that the streamwise perturbations are L2-energy stable for any Reynolds number. This…
We study the monotone energy stability of ``Poiseuille flow" in a plane-parallel channel with a saturated porous medium modeled by the Brinkman equation, on the basis of an analogy with a magneto-hydrodynamic problem (Hartmann flow) (cf.…
In complex power systems, nonlinear load flow equations have multiple solutions. Under typical load conditions only one solution is stable and corresponds to a normal operating point, whereas the second solution is not stable and is never…
We consider the periodic problem for two-fluid non-isentropic Euler-Maxwell systems in plasmas. By means of suitable choices of symmetrizers and an induction argument on the order of the time-space derivatives of solutions in energy…
In this second article of a series we propose to base criteria of stability on the hamiltonian functional that is provided by the variational principle, to replace the reliance that has often been placed on {\it ad hoc} definitions of the…
We introduce a notion of stability for non-autonomous Hamiltonian flows on two-dimensional annular surfaces. This notion of stability is designed to capture the sustained twisting of particle trajectories. The main Theorem is applied to…
Equilibrium statistical mechanics predicts that inviscid, two-dimensional, incompressible flow on the sphere eventually reaches a state in which spherical harmonic modes of degrees $n=1$ and $n=2$ hold all the energy. By a separate theory,…
The paper studies the equilibrium configurations of inextensible elastic membranes exhibiting lateral fluidity. Using a continuum description of the membrane's motions based on the surface Navier--Stokes equations with bending forces, the…
A statistical method for calculating equilibrium solutions of the shallow water equations, a model of essentially 2-d fluid flow with a free surface, is described. The model contains a competing acoustic turbulent {\it direct} energy…
The rimming flow of a viscoelastic thin film inside a rotating horizontal cylinder is studied theoretically. Attention is given to the onset of non-Newtonian free-surface instability in creeping flow. This non-inertial instability has been…
We introduce a new concept of dissipative varifold solution to models of two phase compressible viscous fluids. In contrast with the existing approach based on the Young measure description, the new formulation is variational combining the…
We consider the hydrodynamic evolution of a quark-gluon gas with non-zero quark masses and net baryon number in its phase diagram. For far-off-equilibrium initial conditions the expansion trajectories appear to violate simple rules based on…
Nonlinear waves are studied in a mixture of liquid and gas bubbles. Influence of viscosity and heat transfer is taken into consideration on propagation of the pressure waves. Nonlinear evolution equations of the second and the third order…
Dense granular flows exhibit both surface deformation and secondary flows due to the presence of normal stress differences. Yet, a complete mathematical modelling of these two features is still lacking. This paper focuses on a steady…
We model the flow of a bi-viscous non-Newtonian fluid in a porous medium by a square lattice where the links obey a piece-wise linear constitutive equation. We find numerically that the flow regime where the network transitions from all…
In this note, we derive a stability and weak-strong uniqueness principle for volume-preserving mean curvature flow. The proof is based on a new notion of volume-preserving gradient flow calibrations, which is a natural extension of the…