Related papers: Characterization of three-dimensional Euler flows …
An effort has been made to solve the Cauchy problem of the Navier-Stokes equations in the whole space by two methods. It is proved that the sum of the three vorticity components is a time-invariant in fluid motion. It has been proved that,…
The dynamics along the particle trajectories for the 3D axisymmetric Euler equations are considered. It is shown that if the inflow is rapidly increasing (pushy) in time, the corresponding laminar profile of the incompressible Euler flow is…
We consider a wide class of approximate models of evolution of singular distributions of vorticity in three dimensional incompressible fluids and we show that they have global smooth solutions. The proof exploits the existence of suitable…
In this paper, we perform a careful numerical study of nearly singular solutions of the 3D incompressible Euler equations with smooth initial data. We consider the interaction of two perturbed antiparallel vortex tubes which was previously…
Does three-dimensional incompressible Euler flow with smooth initial conditions develop a singularity with infinite vorticity after a finite time? This blowup problem is still open. After briefly reviewing what is known and pointing out…
In this article, we first consider solutions to a semilinear elliptic problem in divergence form \begin{equation*} \begin{cases} -\varepsilon^2\text{div}(K(x)\nabla u)= (u-q|\ln\varepsilon|)^{p}_+,\ \ &x\in \Omega,\\ u=0,\ \ &x\in\partial…
We establish the existence and uniqueness of some smooth accelerating transonic flows governed by the three dimensional steady compressible Euler equations with an external force in cylinders with arbitrary cross sections, which include…
We consider a two-dimensional, two-layer, incompressible, steady flow, with vorticity which is constant in each layer, in an infinite channel with rigid walls. The velocity is continuous across the interface, there is no surface tension or…
Given any smooth solenoidal vector field $v_0$ on $\mathbf T^3$, we show the existence of infinitely many H\"older-continuous steady Euler flows $v$ with the same topology as $v_0$, in certain weak sense. In particular, we show that $v$…
We consider solutions to the two-dimensional incompressible Euler system with only integrable vorticity, thus with possibly locally infinite energy. With such regularity, we use the recently developed theory of Lagrangian flows associated…
In this paper, we consider the existence of concentrated helical vortices of 3D incompressible Euler equations with swirl. First, without the assumption of the orthogonality condition, we derive a 2D vorticity-stream formulation of 3D…
In Lagrangian turbulence one is faced with the puzzle that 2D Navier-Stokes flows are nearly as intermittent as in three dimensions although no intermittency is present in the inverse cascade in 2D Eulerian turbulence. In addition, an…
We revisit and present new linear spaces of explicit solutions to incompressible Euler and Navier-Stokes equations on $\mathbb{R}^n$, as well as the rotating Boussinesq equations on $\mathbb{R}^3$. We cast these solutions are superpositions…
We present a numerical method of analyzing possibly singular incompressible 3D Euler flows using massively parallel high-resolution adaptively refined numerical simulations up to 8192^3 mesh points. Geometrical properties of Lagrangian…
Generalized Navier-Stokes (GNS) equations describing three-dimensional (3D) active fluids with flow-dependent spectral forcing have been shown to possess numerical solutions that can sustain significant energy transfer to larger scales by…
Characteristics of Oscillating Flow in a Straight Tube with varying thickness of porous layer at the wall is studied. Results for two different porous layer is discussed and compared in terms of Velocity Profile, phase differences and…
We have developed a three-dimensional (3D) spectral hydrodynamic code to study vortex dynamics in rotating, shearing, stratified systems (e.g. the atmosphere of gas giant planets, protoplanetary disks around newly forming protostars). The…
We consider the flow of a Newtonian fluid in a three-dimensional domain, rotating about a vertical axis and driven by a vertically invariant horizontal body-force. This system admits vertically invariant solutions that satisfy the 2D…
Currently, Eulerian flow solvers are very efficient in accurately resolving flow structures near solid boundaries. On the other hand, they tend to be diffusive and to dampen high-intensity vortical structures after a short distance away…
We consider solutions to the complex Trkalian equation,~$ \vec{\nabla} \times \vc = \vc ,$ where~$\vc$ is a 3 component vector function with each component in the complex field, and may be expressed in the form~$ \vc = e^{ig} \vec{\nabla}…