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A b s t r a c t. The initial boundary value problem is considered for the Euler equations for an incompressible fluid in a bounded domain D ⊂ R n. It is known [Y1] that uniqueness holds for those flows with bounded vortic-ity. We present here a uniqueness theorem in some classes (B-spaces) of incompressible flows with vorticity which is unbounded but… (More)

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

— " The diversity of problems exhibited in hydrodynamics alone can only make one admire the inexhaustibility of fascinating problems that occur in nature. " —Birkhoff, Bellman, and Lin, from Hydrodynamic Instability, 1962. O ur everyday life is full of examples of fluid motion, from the drama of tornadoes and hurricanes, the turbulent cascading flows in… (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 initial-boundary value problems in the theory of ideal and viscous incompress-ible fluids, the spectral problems in hydrodynamic stability theory for steady and time… (More)

This paper 3 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)

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

More than 160 years after their invention by Hamilton, quater-nions 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 quaternion-frame — for… (More)

- V N Govorukhin, A Morgulis, V I Yudovich, G M 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)

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