相关论文: Least action principles for incompressible flows a…

There is a remarkable and canonical problem in 3D geometry and topology: To understand existing models of 3D fluid motion or to create new ones that may be useful. We discuss from an algebraic viewpoint the PDE called Euler's equation for…

In this work we study the asymptotic behavior of solutions of the incompressible two-dimensional Euler equations in the exterior of a single smooth obstacle when the obstacle becomes very thin tending to a curve. We extend results by…

We study a family of approximations to Euler's equation depending on two parameters $\varepsilon,\eta \ge 0$. When $\varepsilon=\eta=0$ we have Euler's equation and when both are positive we have instances of the class of…

We consider the classical compressible Euler's Equations in three space dimensions with an arbitrary equation of state, and whose initial data corresponds to a constant state outside a sphere. Under suitable restriction on the size of the…

In this paper, we study the global existence of steady subsonic Euler flows through infinitely long nozzles without the assumption of irrotationality. It is shown that when the variation of Bernoulli's function in the upstream is…

The interplay between incompressibility and stratification can lead to non-conservation of horizontal momentum in the dynamics of a stably stratified incompressible Euler fluid filling an infinite horizontal channel between rigid upper and…

The restriction of hydrodynamics to non-viscous, potential (gradient, irrotational) flows is a theory both simple and elegant; a favorite topic of introductory textbooks. It is known that this theory can be formulated as an action principle…

In this paper, we establish a mathematical theory on statement and validation of the hypersonic similarity law within the framework of Radon measure solutions of steady compressible Euler equations. We consider two scenarios: (1)…

We consider the Euler equations for compressible fluids in a nozzle whose cross-section is variable and may contain discontinuities. We view these equations as a hyperbolic system in nonconservative form and investigate weak solutions in…

We propose in this work new systems of equations which we call $p$-Euler equations and $p$-Navier-Stokes equations. $p$-Euler equations are derived as the Euler-Lagrange equations for the action represented by the Benamou-Brenier…

In this paper we developed an analysis of the compressible, isentropic Euler equations in two spatial dimensions for a generalized polytropic gas law. The main focus is rotational flows in the subsonic regimes, described through the…

Several hydrodynamic models the atomic Bose-Einstein condensate beyond the mean-field approximation are discussed together from one point of view. All these models are derived from microscopic quantum description. The derivation is made…

In this paper, we consider 2D incompressible Euler equations in an unbounded domain with a free surface and a fixed bottom at finite depth. The fluid motion is under the influence of gravity and surface tension. We construct initial data…

In this paper, we study two-dimensional steady incompressible Euler flows in which the vorticity is sharply concentrated in a finite number of regions of small diameter in a bounded domain. Mathematical analysis of such flows is an…

A nontrivial smooth steady incompressible Euler flow in three dimensions with compact support is constructed. Another uncommon property of this solution is the dependence between the Bernoulli function and the pressure.

We consider the Euler equations of incompressible fluids and attempt to solve the initial value problem with the help of a concave maximization problem.We show that this problem, which shares a similar structure with the optimal transport…

We establish the vanishing viscosity limit of the Navier-Stokes equations to the isentropic Euler equations for one-dimensional compressible fluid flow. For the Navier-Stokes equations, there exist no natural invariant regions for the…

We prove a priori estimates for the compressible Euler equations modeling the motion of a liquid with moving physical vacuum boundary in an unbounded initial domain. The liquid is under influence of gravity but without surface tension. Our…

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…

We obtain the local existence and uniqueness for a system describing interaction of an incompressible inviscid fluid, modeled by the Euler equations, and an elastic plate, represented by the fourth-order hyperbolic PDE. We provide a~priori…