Related papers: Theory of Drop Formation
We consider the viscous motion of a thin, axisymmetric column of fluid with a free surface. A one-dimensional equation of motion for the velocity and the radius is derived from the Navier-Stokes equation. We compare with recent experiments…
Singularities of the Navier-Stokes equations occur when some derivative of the velocity field is infinite at any point of a field of flow (or, in an evolving flow, becomes infinite at any point within a finite time). Such singularities can…
The problem of global-in-time regularity for the 3D Navier-Stokes equations, i.e., the question of whether a smooth flow can exhibit spontaneous formation of singularities, is a fundamental open problem in mathematical physics. Due to the…
We develop mathematical methods which allow us to study asymptotic properties of solutions to the three dimensional Navier-Stokes system for incompressible fluid in the whole three dimensional space. We deal either with the Cauchy problem…
We consider the compressible three dimensional Navier Stokes and Euler equations. In a suitable regime of barotropic laws, we construct a set of finite energy smooth initial data for which the corresponding solutions to both equations…
We study the two-dimensional stationary Navier-Stokes equations describing the flows around a rotating obstacle. The unique existence of solutions and their asymptotic behavior at spatial infinity are established when the rotation speed of…
We study the two-dimensional stationary Navier-Stokes equations with rotating effect in the whole space. The unique existence and the asymptotics of solutions are obtained without the smallness assumption on the rotation parameter.
Existence, uniqueness, and regularity of time-periodic solutions to the Navier-Stokes equations in the three-dimensional whole-space are investigated. We consider the Navier-Stokes equations with a non-zero drift term corresponding to the…
The question of whether a singularity can form in an initially regular flow, described by the 3D incompressible Navier-Stokes (NS) equations, is a fundamental problem in mathematical physics. The NS regularity problem is super-critical,…
In fairly general conditions we give explicit (smooth) solutions for the potential flow. We show that, rigorously speaking, the equations of the fluid mechanics have not rotational solutions. However, within the usual approximations of an…
We consider the three-dimensional steady Navier-Stokes system in the exterior of an infinite cylinder under the action of an external force. We construct solutions in the class of vertically uniform flows which vanish at horizontal…
A proof of existence, uniqueness and smoothness of the Navier-Stokes equations is an actual problem, which solution is important for different branches of science. The subject of this study is obtaining the smooth and unique solutions of…
We prove global smooth continuation for smooth finite-energy solutions of the three-dimensional incompressible Navier--Stokes equations by a two-part first-threshold argument. Part I proves the axisymmetric-with-swirl theorem in the exact…
Droplet formation happens in finite time due to the surface tension force. The linear stability analysis is useful to estimate droplet size but fails to approximate droplet shape. This is due to a highly non-linear flow description near the…
On one hand, classical Monte Carlo and molecular dynamics (MD) simulations have been very useful in the study of liquids in nanotubes, enabling a wide variety of properties to be calculated in intuitive agreement with experiments. On the…
We present a formal, approximate model for singularity formation in classical fluid dynamics in three dimensions. The construction utilizes an approximation of local two-dimensionality to study an anti-parallel hairpin vortex structure with…
The one-dimensional Navier-Stokes equations are used to derive analytical expressions for the relation between pressure and volumetric flow rate in capillaries of five different converging-diverging axisymmetric geometries for Newtonian…
We establish pointwise decay estimates for the velocity field of a steady two-dimensional Stokes flow around a rotating body via a new approach rather than analysis adopted in the previous literature. The novelty is to analyze the singular…
Attention has been paid to the similarity and duality between the Gregory-Laflamme instability of black strings and the Rayleigh-Plateau instability of extended fluids. In this paper, we derive a set of simple (1+1)-dimensional equations…
The Navier-Stokes equation can be written in a form of Poisson equation. For laminar flow in a channel (plane Poiseuille flow), the Navier-Stokes equation has a non-zero source term and a non-zero solution within the domain. For…