Related papers: A free boundary inviscid model of flow-structure i…
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…
We concern with the global existence and large time behavior of compressible fluids (including the inviscid gases, viscid gases, and Boltzmann gases) in an infinitely expanding ball. Such a problem is one of the interesting models in…
In this work we analyze the stability and convergence properties of a loosely-coupled scheme, called the kinematically coupled scheme, for interaction between an incompressible viscous fluid and a thin structure. We consider a benchmark…
In this paper, we investigate the initial value problem for the Euler-Riesz system, where the interaction forcing is given by $\nabla(-\Delta)^{s}\rho$ for some $-1<s<0$, with $s = -1$ corresponding to the classical Euler-Poisson system. We…
Properties of an infinite system of nonlinearly coupled ordinary differential equations are discussed. This system models some properties present in the equations of motion for an inviscid fluid such as the skew symmetry and the…
We prove that, in a two-dimensional strip, a steady flow of an ideal incompressible fluid with no stationary point and tangential boundary conditions is a shear flow. The same conclusion holds for a bounded steady flow in a half-plane. The…
We consider the free-boundary motion of two perfect incompressible fluids with different densities $\rho_+$ and $\rho_-$, separated by a surface of discontinuity along which the pressure experiences a jump proportional to the mean curvature…
We consider two models of a compressible inviscid isentropic two-fluid flow. The first one describes the liquid-gas two-phase flow. The second one can describe the mixture of two fluids of different densities or the mixture of fluid and…
We study a nonlinear, moving boundary fluid-structure interaction problem between an incompressible, viscous Newtonian fluid, modeled by the 2D Navier-Stokes equations, and an elastic structure modeled by the shell or plate equations. The…
We derive a priori estimates for the compressible free boundary Euler equations in the case of a liquid without surface tension. We provide a new weighted functional framework which leads to the improved regularity of the flow map by using…
We study singular limit for scaled barotropic Euler system modelling a rotating, compressible and inviscid fluid, where Mach and Rossby numbers are proportional to a small parameter $\epsilon$. If the fluid is confined to an infinite slab,…
A semi-explicit formula of solution to the boundary layer system for thermal layer derived from the compressible Navier-Stokes equations with the non-slip boundary condition when the viscosity coefficients vanish is given, in particular in…
Consider a free boundary problem of compressible-incompressible two-phase flows with surface tension and phase transition in bounded domains $\Omega_{t +}, \Omega_{t -} \subset \mathbb{R}^N$, $N \ge 2$, where the domains are separated by a…
We prove a local existence theorem for the free boundary problem for a relativistic fluid in a fixed spacetime. Our proof involves an a priori estimate which only requires control of derivatives tangential to the boundary, which holds also…
We investigate a hydrodynamic system of Navier--Stokes/Cahn--Hilliard type, which describes the motion of a two-phase flow of two incompressible fluids with unmatched densities coupled with a soluble chemical species. Derived from Onsager's…
In this article, we prove the local well-posedness of the free-boundary Lin-Liu equations describing the motion of inviscid nematic liquid crystals in the presence of surface tension in Lagrangian coordinates. It is well known that a priori…
In this two-parts paper, we present a systematic procedure to extend the known Hamiltonian model of ideal inviscid fluid flow on Riemannian manifolds in terms of Lie-Poisson structures to a port-Hamiltonian model in terms of Stokes-Dirac…
In this paper a new monolithic Eulerian formulation in the framework of non-classical continuum is presented for the analysis of fluid-strucuture interaction problems. In this respect, Cosserat continuum theory taking into account the…
Interfacial instability is highly relevant to many important biological processes. A key example arises in wound healing experiments, which observe that an epithelial layer with an initially straight edge does not heal uniformly. We…
This article deals with the issues of global-in-time existence and asymptotic analysis of a fluid-particle interaction model in the so-called bubbling regime. The mixture occupies the physical space $\Omega \subset \mathbb{R}^3$ which may…