相关论文: On the dispersion relation for compressible Navier…

We consider the initial value problem of the compressible Navier-Stokes-Korteweg equations in the whole space $\mathbb{R}^d$ ($d \ge 2$). The purposes of this paper are to obtain the global-in-time solution around the constant equilibrium…

It is shown that thermal fluctuations present in a simple non-degenerate relativistic fluid satisfy a wave equation in the Euler regime. The characteristic propagation speeds are calculated and the classical expression for the speed of…

We introduce a diffuse interface model describing the evolution of a mixture of two different viscous incompressible fluids of equal density. The main novelty of the present contribution consists in the fact that the effects of temperature…

We study the propagation of acoustic waves in a fluid that is contained in a thin two-dimensional tube, and that it is moving with a velocity profile that only depends on the transversal coordinate of the tube. The governing equations are…

Understanding how molecules engage in collective motions in a liquid where a network of bonds exists has both fundamental and applied relevance. On the one hand, it can elucidate the ``ordering" role of long-range correlations in an…

We study the propagation of a density wave in a magnetically trapped Bose-Einstein condensate at finite temperatures. The thermal cloud is in the hydrodynamic regime and the system is therefore described by the two-fluid model. A…

In this paper, we first present a Gearhardt-Pr\"uss type theorem with a sharp bound for m-accretive operators. Then we give two applications: (1) give a simple proof of the result proved by Constantin et al. on relaxation enhancement…

Fluid equations are nonlinear, dissipative, and non-Hamiltonian, which makes their relation to Schr\"odinger evolution and quantum algorithms nontrivial. We derive an exact Eulerian Cole-Hopf-type reformulation of isothermal compressible…

The very long standing problem of sound waves propagation in fluids is reexamined. In particular, from the analysis of the wave damping in reacting gases following the work of Einsten \citep{Ein}, it is found that the damping due to the…

We explore the scattering amplitudes of fluid quanta described by the Navier-Stokes equation and its non-Abelian generalization. These amplitudes exhibit universal infrared structures analogous to the Weinberg soft theorem and the Adler…

Stokes flow equations, used to model creeping flow, are a commonly used simplification of the Navier--Stokes equations. The simplification is valid for flows where the inertial forces are negligible compared to the viscous forces. In…

We develop a unified theory for the second sound in two dimensional materials. Previously studied drifting and driftless second sound are two limiting cases of the theory, corresponding to the drift and diffusive part of the energy flux,…

We consider density fluctuations of a two-fluid model consisting of hydrogen plasma and radiation prior to the cosmic hydrogen recombination. As investigation method that of the dispersion relations is applied, which have been derived from…

Diffraction is a phenomenon, discussed for centuries from various points of view. The very simple principle, proposed by Huygens [1] and then modified by Fresnel[2], Stokes [3] and Kirchoff [4], allows us to make calculations, substituting…

We discuss the collective excitations in a spatially inhomogeneous (cylindrically symmetric) Bose-Einstein condensation (BEC) at low temperature ($T \ll T_{\lambda}$). The main result is the dispersion relation for a (first) sound wave that…

We study the time-harmonic Galbrun equation describing the propagation of sound in the presence of a steady background flow. With additional rotational and gravitational terms these equations are also fundamental in helio- and…

Acoustic fields effect steady transport of suspended particles by rectifying the inertia of primary oscillations. We develop a fully analytic theory that relates this steady particle motion to incident oscillatory (acoustic) flow and the…

We prove a stability threshold theorem for 2D Navier-Stokes on three unbounded domains: the whole plane $\mathbb{R} \times \mathbb{R}$, the half plane $\mathbb{R} \times [0,\infty)$ with Navier boundary conditions, and the infinite channel…

The system of Navier--Stokes--Fourier equations is one of the most celebrated systems of equations in modern science. It describes dynamics of fluids in the limit when gradients of density, velocity and temperature are sufficiently small,…

Sound attenuation in low temperature amorphous solids originates from their disordered structure. However, its detailed mechanism is still being debated. Here we analyze sound attenuation starting directly from the microscopic equations of…