Related papers: Plane waves in noncommutative fluids
We present experimental results on hydrothermal waves in long and narrow 1D channels. In a bounded channel, we describe the primary and secondary instabilities leading to waves and modulated waves in terms of convective/absolute…
The continuum equations of fluid mechanics are rederived with the intention of keeping certain mechanical and thermodynamic concepts separate. A new "mechanical" mass density is created to be used in computing inertial quantities, whereas…
We determine the energy-momentum tensor of non-perfect fluids in thermodynamic equilibrium. To this end, we derive the constitutive equations for energy density, isotropic and anisotropic pressure as well as for heat-flux from the…
This paper presents the second-order perturbation theory of the Navier-Stokes equations for free surface flows, with the wave amplitude considered as the perturbation parameter. Gravity-capillary surface waves in incompressible viscous…
We study mathematically a system of partial differential equations arising in the modelling of an aging fluid, a particular class of non Newtonian fluids. We prove well-posedness of the equations in appropriate functional spaces and…
A variational principle is derived for two-dimensional incompressible rotational fluid flow with a free surface in a moving vessel when both the vessel and fluid motion are to be determined. The fluid is represented by a stream function and…
In this paper we discuss the motion of a beam in interaction with fluids. We allow the beam to move freely in all coordinate directions. We consider the case of a beam situated in between two different fluids as well as the case where the…
We consider a boundary value problem for the system of equations describing the stationary motion of a viscous nonhomogeneous asymmetric fluid in a bounded planar domain having a $C^2$ boundary. We use a stream-function formulation after…
This paper concerns the construction of traveling wave solutions to the free boundary incompressible Navier-Stokes system. We study a single layer of viscous fluid in a strip-like domain that is bounded below by a flat rigid surface and…
We introduce a three independent functions variational formalism for stationary and non-stationary barotropic flows. This is less than the four variables which appear in the standard equations of fluid dynamics which are the velocity field…
We investigate analytically the propagation of linear waves in a three-dimensional, nonmagnetic, isothermal atmosphere stratified in plane-parallel layers. The motivation is to study oscillations in the non-magnetic chromosphere and to…
Nonlinear excitations of nuclear density are considered in the framework of semiclassical nonlinear nuclear hydrodynamics. Possible types of stationary nonlinear waves in nuclear media are analysed using Nonlinear Schroedinger equation of…
We study a coupled kinetic-non-Newtonian fluid system on the periodic domain ${\mathbb T}^3$, where particles evolve by a Vlasov equation and interact with an incompressible power-law fluid through a drag force. We prove the global…
The flow of the relativistic imperfect fluid in two dimensions is discussed. We calculate the symmetry group of the energy-momentum tensor conservation equation in the ultrarelativistic limit. Group-invariant solutions for the…
We consider a system of two discrete nonlinear Schr\"{o}dinger equations, coupled by nonlinear and linear terms. For various physically relevant cases, we derive a modulational instability criterion for plane-wave solutions. We also find…
A two-dimensional water wave system is examined consisting of two discrete incompressible fluid domains separated by a free common interface. In a geophysical context this is a model of an internal wave, formed at a pycnocline or…
We show that equations of Newtonian hydrodynamics and gravity describing one-dimensional steady gas flow possess nonlinear periodic solutions. In the case of a zero-pressure gas the solution exhibits hydrodynamic similarity and is…
This work is directed towards investigating the fate of three-dimensional long perturbation waves in a plane incompressible wake. The analysis is posed as an initial-value problem in space. More specifically, input is made at an initial…
Following a recent demonstration of stable trapping of floating particles by stationary (monochromatic) structured water waves [Nature 638, 394 (2025)], we report dynamic water-wave tweezers that enable controllable transport of trapped…
We consider a linear system that consists of a linear wave equation on a horizontal hypersurface and a parabolic equation in the half space below. The model describes longitudinal elastic waves in organic monolayers at the water-air…