#### Filter Results:

- Full text PDF available (8)

#### Publication Year

1995

2011

- This year (0)
- Last 5 years (0)
- Last 10 years (3)

#### Publication Type

#### Co-author

#### Journals and Conferences

#### Key Phrases

Learn More

- Victor Yudovich, Victor Yudovich, Gérard Gé
- 1995

A bstract . The initial boundary value problem is considered for the Euler equations for an incompressible fluid in a bounded domain D ⊂ Rn. It is known [Y1] that uniqueness holds for those flows with bounded vorticity. We present here a uniqueness theorem in some classes (B-spaces) of incompressible flows with vorticity which is unbounded but belongs to… (More)

- L. Belenkaya, Susan Friedlander, Victor Yudovich
- SIAM Journal of Applied Mathematics
- 1999

1358 NOTICES OF THE AMS VOLUME 46, NUMBER 11 O ur everyday life is full of examples of fluid motion, from the drama of tornadoes and hurricanes, the turbulent cascading flows in rivers, and the breaking of massive ocean waves to the undramatic familiarity of stirring a cup of tea. Inspired by observation, scientists have sought for centuries to understand… (More)

The key unsolved problems of mathematical fluid dynamics, their current state and outlook are discussed. These problems concern global existence and uniquness theorems for basic boundary and initialboundary value problems in the theory of ideal and viscous incompressible fluids, the spectral problems in hydrodynamic stability theory for steady and time… (More)

- Victor Yudovich, John D. Gibbon, William Rowan Hamil
- 2007

More than 160 years after their invention by Hamilton, quaternions are now widely used in the aerospace and computer animation industries to track the orientation and paths of moving objects undergoing three-axis rotations. Here it is shown that they provide a natural way of selecting an appropriate orthonormal frame—designated the quaternionframe— for a… (More)

We study the unstable spectrum of an equation that arises in geophysical fluid dynamics known as the surface quasi-geostrophic equation. In general the spectrum is the union of discrete eigenvalues and an essential spectrum. We demonstrate the existence of unstable eigenvalues in a particular example. We examine the spectra of the semigroup and the… (More)

In Part I, we construct a class of examples of initial velocities for which the unique solution to the Euler equations in the plane has an associated flow map that lies in no Hölder space of positive exponent for any positive time. In Part II, we explore inverse problems that arise in attempting to construct an example of an initial velocity producing an… (More)

Consider a dynamical system generated by a quadratic mapping of the plane (x, y) 7−→ (λx + xy, μy + x) with parameters λ, μ ∈ R. This 2-parameter family arises as a finite-difference approximation of an ODE system with special quadratic nonlinearity and also as a leading part of a map on a center manifold (in some problems of intersections of bifurcations).… (More)

- Vasily N. Govorukhin, Andrey Morgulis, Victor Yudovich, George Zaslavsky
- Physical review. E, Statistical physics, plasmas…
- 1999

Compressible helical flow with div v not equal to 0 drastically increases the area of chaotic dynamics and mixing properties when the helicity parameter is spatially dependent. We show that the density dependence on the z coordinate can be incorporated in new variables in a way that leads to a Hamiltonian formulation of the system. This permits the… (More)

This paper provides a new insight into the classical Björkness problem. We examine system ‘solid+fluid’ forced by an immobile singlet whose intensity is given at every time. We show that this system is governed by the Least Action Principle. The related Largangian is written out almost explicitly up to the Green function of the solid. In particular, there… (More)

- ‹
- 1
- ›