相关论文: Variational formulations of sound-proof models

A fluid described by an Abelian Chern-Simons action principle in 4+1 dimensions is considered. Letting 3+1 dimensions correspond to the usual space and time, and assuming the fields to be independent of the fifth coordinate, the free theory…

Hamilton's principle plays a central role in fluid mechanics as a fundamental tool for deriving governing equations, analyzing conservation laws, and designing structure-preserving numerical schemes. However, its classical formulation is…

In this work, we design and analyze semi/fully-discrete virtual element approximations for the time-dependent Navier--Stokes-Cahn--Hilliard equations, modeling the dynamics of two-phase incompressible fluid flows with diffuse interfaces. A…

For the water-air system, the bulk density ratio is as high as about 1000; no model can fully tackle such a high density ratio system. In the Navier-Stokes and Euler equations, the density $\rho$ within the water-air interface is assumed to…

Thin astrophysical discs are very often modelled using the equations of two-dimensional hydrodynamics. We derive an extension of this model that describes more accurately the behaviour of a thin disc in the absence of self-gravity, magnetic…

Numerical simulations of compressible real-fluid flows are notoriously plagued by spurious pressure oscillations arising in regions of abrupt flow variations. As a possible remedy, several numerical formulations enforce the pressure…

By means of a unifying measure-theoretic approach, we establish lower bounds on the Hausdorff dimension of the space-time set which can support anomalous dissipation for weak solutions of fluid equations, both in the presence or absence of…

We give a sufficient condition for the nonlinear stability of steady flows of a two-dimensional ideal fluid in a bounded multiply-connected domain, which generalizes a stability criterion proved by Arnold in the 1960s. The most important…

The incompressible Navier-Stokes equations contain viscous dissipation but no thermal noise. I show, using a topological argument based on Poincar\'e's lemma, that the fluctuation-dissipation relation for the full nonlinear dynamics can be…

We study the vanishing dissipation limit of the three-dimensional (3D) compressible Navier-Stokes-Fourier equations to the corresponding 3D full Euler equations. Our results are twofold. First, we prove that the 3D compressible…

These lecture notes in geometric mechanics are meant to convey insight through clear definitions and workable examples. The lecture format adopted here is intended to convey the immediacy of the taught course and to be useful as a basis for…

This study derives geometric, variational discretizations of continuum theories arising in fluid dynamics, magnetohydrodynamics (MHD), and the dynamics of complex fluids. A central role in these discretizations is played by the geometric…

We present a new variational principle for the gyrokinetic system, similar to the Maxwell-Vlasov action presented in Ref. 1. The variational principle is in the Eulerian frame and based on constrained variations of the phase space fluid…

The Lagrangian average (LA) of the ideal fluid equations preserves their fundamental transport structure. This transport structure is responsible for the Kelvin circulation theorem of the LA flow and, hence, for its potential vorticity…

This paper concerns the well-posedness of subsonic Euler-Poisson flows in a convergent nozzle. Due to the geometry of the nozzle, we first introduce a coordinate transformation to prove the existence of radially symmetric subsonic solutions…

It has been demonstrated that the Euler equations of inviscid fluid are incomplete: according to the principle of release of constraints, absence of shear stresses must be compensated by additional degrees of freedom, and leads to…

We construct the noncanonical Poisson bracket associated with the phase space of first order moments of the velocity field and quadratic moments of the density of a fluid with a free- boundary, constrained by the condition of…

Recently, the phenomena of streaming suppression and relocation of inhomogeneous miscible fluids under acoustic fields were explained using the hypothesis on mean Eulerian pressure. In this letter, we show that this hypothesis is unsound…

In traditional hydrodynamic theories for ionic fluids, conservation of the mass and linear momentum is not properly taken care of. In this paper, we develop hydrodynamic theories for a viscous, ionic fluid of $N$ ionic species enforcing…

We consider the inhomogeneous incompressible Euler equations including their local energy inequality as a differential inclusion. Providing a corresponding convex integration theorem and constructing subsolutions, we show the existence of…