Related papers: On global multidimensional supersonic flows with v…
In this paper, we consider the 3-D steady potential flow for a compressible gas with pressure satisfying $p'(\rho)=\rho^{\gamma-1}$, where $\rho$ is the density and $\gamma\geq-1$ is a constant. In spherical coordinates, the potential…
We consider a thermodynamically consistent diffuse interface model describing two-phase flows of incompressible fluids in a non-isothermal setting. This model was recently introduced in a previous paper of ours, where we proved existence of…
Understanding the dynamics and stability of transonic flows in quantum fluids, especially for those beyond one spatial dimension, is an outstanding challenge, with applications ranging from nonlinear optics and condensed matter to analogue…
In this paper, we prove the structural stability of the transonic shocks for three dimensional axisymmetric Euler system with swirl velocity under the perturbations for the incoming supersonic flow, the nozzle boundary, and the exit…
We introduce a notion of stability for non-autonomous Hamiltonian flows on two-dimensional annular surfaces. This notion of stability is designed to capture the sustained twisting of particle trajectories. The main Theorem is applied to…
In this article we consider the inviscid two-dimensional shallow water equations in a rectangle. The flow occurs near a stationary solution in the so called supercritical regime and we establish short term existence of smooth solutions for…
The present paper considers the full nonlinear dynamics of a homogeneous bubble inside an unbounded isentropic compressible inviscid liquid. This model is described by a free-boundary problem of compressible Euler equations with nonlinear…
Incompressible Euler flows in narrow domains, in which the horizontal length scale is much larger than other scales, play an important role in applications, and their leading-order behavior can be described by the hydrostatic Euler…
In this paper, we are concerned with the existence of transonic shock solutions for two-dimensional (2-d) steady Euler flows of polytropic gases with the vertical gravity in a horizontal nozzle under a pressure condition imposed at the exit…
We consider the stationary flow of an inviscid and incompressible fluid of constant density in the region $D=(0, L)\times \mathbb{R}^2$. We are concerned with flows that are periodic in the second and third variables and that have…
In this paper, we establish the existence of three-dimensional axisymmetric compressible jet flows for steady Euler system with large vorticity by using the variational method. More precisely, for given axial velocity of the flow at the…
In this paper we develop a theory for an infinitely long droplet state of a zero temperature dipolar bosonic gas. The infinite droplet theory yields simpler equations to solve for the droplet state and its collective excitations. We explore…
We consider a class of abstract quasilinear parabolic problems with lower--order terms exhibiting a prescribed singular structure. We prove well--posedness and Lipschitz continuity of associated semiflows. Moreover, we investigate global…
For one dimensional or multidimensional compressible Euler system of polytropic gases, it is well known that the smooth solution will generally develop singularities in finite time. However, for three dimensional Chaplygin gases, due to the…
We investigate the incompressible Navier-Stokes equations with variable density. The aim is to prove existence and uniqueness results in the case of discontinuous ini- tial density. In dimension n = 2, 3, assuming only that the initial…
We study the dynamics of dilute and ultracold bosonic gases in a quasi two-dimensional (2D) configuration and in the collisionless regime. We adopt the 2D Landau-Vlasov equation to describe a three-dimensional gas under very strong harmonic…
We give a short proof of the existence of a small piece of null infinity for $(3+1)$-dimensional spacetimes evolving from asymptotically flat initial data as solutions of the Einstein vacuum equations. We introduce a modification of the…
In this letter we develop a theory for the first and second sound in a two-dimensional atomic superfluid across the superfluid transition based on the dynamic Koterlitz-Thouless theory. We employ a set of modified two-fluid hydrodynamic…
We develop a method that works in general product Riemannian manifold to decompose the three-dimensional steady full compressible Euler system, which is of elliptic-hyperbolic composite-mixed type for subsonic flows. The method is applied…
We consider the Nernst-Planck-Stokes system on a bounded domain of $\mathbb{R}^d$, $d=2,3$ with general nonequilibrium Dirichlet boundary conditions for the ionic concentrations. It is well known that, in a wide range of cases, equilibrium…