Related papers: Euler equations on a fast rotating sphere --- time…
We investigate exact nonlinear waves on surfaces locally approximating the rotating sphere for two-dimensional inviscid incompressible flow. Our first system corresponds to a beta-plane approximation at the equator and the second to a gamma…
We consider steady solutions to the incompressible Euler equations in a two-dimensional channel with rigid walls. The flow consists of two periodic layers of constant vorticity separated by an unknown interface. Using global bifurcation…
We prove the existence of local-in-time smooth solutions of the incompressible semi-geostrophic equations expressed in Eulerian co-ordinates in 3-dimensional smooth bounded simply-connected domains. Our solutions adhere to Cullen's…
The dynamics along the particle trajectories for the 3D axisymmetric Euler equations in an infinite cylinder are considered. It is shown that if the inflow-outflow is rapidly increasing in time, the corresponding laminar profile of the…
In the present paper, we study the fast rotation limit for the density-dependent incompressible Euler equations in two space dimensions with the presence of the Coriolis force. In the case when the initial densities are small perturbation…
We provide a integration of Navier-Stokes equations concerning the unsteady-state laminar flow of an incompressible, isothermal (newtonian) fluid in a cylindrical vessel spinning about its symmetry axis, say $z$, and inside which the liquid…
We present a semi-Lagrangian characteristic mapping method for the incompressible Euler equations on a rotating sphere. The numerical method uses a spatio-temporal discretization of the inverse flow map generated by the Eulerian velocity as…
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…
The dynamics along the particle trajectories for the 3D axisymmetric Euler equations in an infinite cylinder are considered. It is shown that if the inflow-outflow is highly oscillating in time, the corresponding Euler flow cannot keep the…
We consider the Euler system set on a bounded convex planar domain, endowed with impermeability boundary conditions. This system is a model for the barotropic mode of the Primitive Equations on a rectangular domain. We show the existence of…
A recent prominent result asserts that steady incompressible Euler flows strictly away from stagnation in a two-dimensional infinitely long strip must be shear flows. On the other hand, flows with stagnation points, very challenging in…
Arnold pointed out that the Euler equation of incompressible ideal hydrodynamics describes geodesics on the group of volume-preserving diffeomorphisms. A simple analogue is the Euler equation for a rigid body, which is the geodesic equation…
We are concerned with global steady subsonic flows through general infinitely long nozzles for the full Euler equations. The problem is formulated as a boundary value problem in the unbounded domain for a nonlinear elliptic equation of…
Within the class of nonlinear hyperbolic balance laws posed on a curved spacetime (endowed with a volume form), we identify a hyperbolic balance law that enjoys the same Lorentz invariance property as the one satisfied by the Euler…
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…
The coupling between dilatation and vorticity, two coexisting and fundamental processes in fluid dynamics is investigated here, in the simplest cases of inviscid 2D isotropic Burgers and pressureless Euler-Coriolis fluids respectively…
We consider an inverse problem for the compressible Euler's equations in polytropic fluid. We show that by taking active measurements near a particle trajectory one can determine the background flow in a set where pressure waves can…
We present a steady Euler flow on the round 3-sphere whose velocity vector field has the property of having two independent first integrals, being tangent to the fibres of an almost submersion onto the 2-sphere. This submersion turns out to…
We examine the blow-up claims of the incompressible Euler equations for several specific flow-fields, (1) the columnar eddies in the vicinity of stagnation; (2) a quasi-three-dimensional structure for illustrating oscillations and…
Euler equations are the basic system in fluid dynamics describing the motion of incompressible and inviscid ideal fluids. For a bounded smooth domain $\Omega$ in $\mathbb{R}^n$. The well-posedness of Euler equations is well-known in Sobolev…