相关论文: Construction of the free-boundary 3D incompressibl…

We consider the three-dimensional Euler equations in a domain with a free boundary with no surface tension. We assume that $u_0 \in H^{2.5+\delta }$ is such that $\mathrm{curl}\,u_0 \in H^{2+\delta }$ in an arbitrarily small neighborhood of…

We consider the three-dimensional incompressible free-boundary Euler equations in a bounded domain and with surface tension. Using Lagrangian coordinates, we establish a priori estimates for solutions with minimal regularity assumptions on…

The 3D incompressible Euler equation is an important research topic in the mathematical study of fluid dynamics. Not only is the global regularity for smooth initial data an open issue, but the behaviour may also depend on the presence or…

We establish a result concerning the so-called Lagrangian controllability of the Euler equation for incompressible perfect fluids in dimension 3. More precisely we consider a connected bounded domain of R^3 and two smooth contractible sets…

The 3D incompressible Euler equations in a bounded domain are most often supplemented with impermeable boundary conditions, which constrain the fluid to neither enter nor leave the domain. We establish well-posedness with inflow, outflow of…

We derive a priori estimates for the incompressible free-boundary Euler equations with surface tension in three spatial dimensions. Working in Lagrangian coordinates, we provide a priori estimates for the local existence when the initial…

In this paper, we study the 2D free boundary incompressible Euler equations with surface tension, where the fluid domain is periodic in $x_1$, and has finite depth. We construct initial data with a flat free boundary and arbitrarily small…

We consider the evolution of an incompressible two-dimensional perfect fluid as the boundary of its domain is deformed in a prescribed fashion. The flow is taken to be initially steady, and the boundary deformation is assumed to be slow…

We prove that the 3-D free-surface incompressible Euler equations with regular initial geometries and velocity fields have solutions which can form a finite-time "splash" (or "splat") singularity first introduced in [9], wherein the…

This paper investigates an incompressible steady free boundary problem of Euler equations with helical symmetry in $3$ dimensions and with nontrivial vorticity. The velocity field of the fluid arises from the spiral of its velocity within a…

We derive a priori estimates for the compressible free-boundary Euler equations with surface tension in three spatial dimensions in the case of a liquid. These are estimates for local existence in Lagrangian coordinates when the initial…

In this paper we derive estimates to the free boundary problem for the Euler equation with surface tension, and without surface tension provided the Rayleigh-Taylor sign condition holds. We prove that as the surface tension tends to zero,…

We study the free boundary problem for the flow of a compressible isentropic inviscid elastic fluid. At the free boundary moving with the velocity of the fluid particles the columns of the deformation gradient are tangent to the boundary…

We consider the free boundary problem for the incompressible elastodynamics equations. At the free boundary moving with the velocity of the fluid particles the columns of the deformation gradient are tangent to the boundary and the pressure…

We consider a free-boundary problem for the incompressible elastodynamics describing the motion of an elastic medium in a periodic domain with a moving boundary and a fixed bottom under the influence of surface tension. The local…

We address the existence and of solutions for the Euler-plate free-boundary system modeling an interaction of a three-dimensional inviscid fluid and an evolving plate. We prove the local existence and uniqueness of solutions for initial…

In this paper we present some classification results for the steady Euler equations in two-dimensional exterior domains with free boundaries. We prove that, in an exterior domain, if a steady Euler flow devoid of interior stagnation points…

We prove that the 3-D compressible Euler equations with surface tension along the moving free-boundary are well-posed. Specifically, we consider isentropic dynamics and consider an equation of state, modeling a liquid, given by Courant and…

In this paper we obtain natural boundary conditions for a large class of variational problems with free boundary values. In comparison with the already existing examples, our framework displays complete freedom concerning the topology of…

We consider the stability of transonic contact discontinuity for the two-dimensional steady compressible Euler flows in a finitely long nozzle. This is the first work on the mixed-type problem of transonic flows across a contact…