Related papers: Looking at bare transport coefficients in fluctuat…
We consider the slow flow of a viscous incompressible liquid in a channel of constant but arbitrary cross section shape, driven by non-uniform suction or injection through the porous channel walls. A similarity transformation reduces the…
The hydrodynamics for a gas of hard-spheres which sometimes experience inelastic collisions resulting in the loss of a fixed, velocity-independent, amount of energy $\Delta $ is investigated with the goal of understanding the coupling…
The incompressible Navier-Stokes (NS) equation is known to govern the hydrodynamic limit of essentially any fluid and its rich non-linear structure has critical implications in both mathematics and physics. The employability of the methods…
Understanding the emergence of macroscopic irreversible hydrodynamics from the reversible unitary dynamics of isolated quantum many-body systems remains a fundamental challenge. Conventional approaches often force spin density dynamics into…
We show that in bounded domains with no-slip boundary conditions, the Navier-Stokes pressure can be determined in a such way that it is strictly dominated by viscosity. As a consequence, in a general domain we can treat the Navier-Stokes…
A simulation of the hydrodynamics on the two dimensional non-commutative space is performed, in which the space coordinates $(x, y)$ are non-commutative, satisfying the commutation relation $[x, y]=i \theta$. The Navier-Stokes equation has…
We show the existence of weak solutions to the fluid-structure interaction problem of a largely deforming viscoelastic bulk solid with a viscous fluid governed by the incompressible Navier-Stokes equations. In contrast to previous works,…
Hydrodynamics can be formulated as the gradient expansion of conserved currents in terms of the fundamental fields describing the near-equilibrium fluid flow. In the relativistic case, the Navier-Stokes equations follow from the…
Visco-resistive magnetohydrodynamic turbulence, driven by a two-dimensional unstable shear layer that is maintained by an imposed body force, is examined by decomposing it into dissipationless linear eigenmodes of the initial profiles. The…
From the Navier-Stokes-Korteweg (NSK) equations, the exact relations between the fundamental surface physical quantities for two-phase viscous flow with diffuse interface are derived, including density gradient, shear stress, vorticity,…
In the present work we compute the enhancement in the long time transport coefficients due to correlated motion of fluid particles at high density. The fully wave vecor dependent extended mode coupling model is studied with the inclusion of…
Singularities of the Navier-Stokes equations occur when some derivative of the velocity field is infinite at any point of a field of flow (or, in an evolving flow, becomes infinite at any point within a finite time). Such singularities can…
We analyze the representation of viscous stresses in the one-fluid formulation of the two-phase Navier-Stokes equations, the model on which all computational approaches making use of a fixed mesh to discretize the flow field are grounded.…
Governing equations of motion for a viscous incompressible material surface are derived from the balance laws of continuum mechanics. The surface is treated as a time-dependent smooth orientable manifold of codimension one in an ambient…
We propose a theoretical framework where the dissipative structures of turbulence emerge from microscopic path uncertainty. By modeling fluid parcels as stochastic tracers governed by the Schr\"odinger Bridge (SB) variational principle, we…
Despite the physical importance, there are limited mathematical theories for the compressible Navier-Stokes equations with strong boundary layers. This is mainly due to the absence of a stream function structure, unlike the extensively…
It is shown that the hydrodynamic modes of a dilute granular gas of inelastic hard spheres can be identified, and calculated in the long wavelength limit. Assuming they dominate at long times, formal expressions for the Navier-Stokes…
We investigate shear-induced crystallization in a very dense flow of mono-disperse inelastic hard spheres. We consider a steady plane Couette flow under constant pressure and neglect gravity. We assume that the granular density is greater…
We introduce an analogue to Kato's Criterion regarding the inviscid convergence of stochastic Navier-Stokes flows to the strong solution of the deterministic Euler equation. Our assumptions cover additive, multiplicative and transport type…
We derive the Hydrodynamics for a system of N active, spherical, underdamped particles, interacting through conservative forces. At the microscopic level, we represent the evolution of the particles in terms of the Kramers equation for the…