Victor Yudovich

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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)
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)
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)
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)
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)
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