Search Results - "Shvydkoy, R."

Convex integration for a class of active scalar equations by SHVYDKOY, R.

“…We show that a general class of active scalar equations, including porous media and certain magnetostrophic turbulence models, admits non-unique weak solutions…”
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The energy balance relation for weak solutions of the density-dependent Navier–Stokes equations by Leslie, T.M., Shvydkoy, R.

“…We consider the incompressible inhomogeneous Navier–Stokes equations with constant viscosity coefficient and density which is bounded and bounded away from…”
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Energy Conservation in Two-dimensional Incompressible Ideal Fluids by Cheskidov, A., Filho, M. C. Lopes, Lopes, H. J. Nussenzveig, Shvydkoy, R.

“…This note addresses the issue of energy conservation for the 2D Euler system with an L p -control on vorticity. We provide a direct argument, based on a…”
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ILL-POSEDNESS OF THE BASIC EQUATIONS OF FLUID DYNAMICS IN BESOV SPACES by CHESKIDOV, A., SHVYDKOY, R.

“…We give a construction of a divergence-free vector field U₀ Є Hs∩ $B_\infty ^{ - 1} _{\infty ,} $ for all s < 1/2, with arbitrarily small norm $||u_0…”
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A Unified Approach to Regularity Problems for the 3D Navier-Stokes and Euler Equations: the Use of Kolmogorov’s Dissipation Range by Cheskidov, A., Shvydkoy, R.

“…Motivated by Kolmogorov’s theory of turbulence we present a unified approach to the regularity problems for the 3D Navier-Stokes and Euler equations. We…”
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Geometric Aspects of the Daugavet Property by Shvydkoy, R.V.

“…Let X be a closed subspace of a Banach space Y and J be the inclusion map. We say that the pair (X, Y) has the Daugavet property if for every rank one bounded…”
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The Largest Linear Space of Operators Satisfying the Daugavet Equation in L1 by Shvydkoy, R. V.

“…We find the largest linear space of bounded linear operators on L1(Ω) that, being restricted to any$L_1(A), A \subset \Omega$, satisfy the Daugavet equation…”
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A Geometric Condition Implying an Energy Equality for Solutions of the 3D Navier–Stokes Equation by Shvydkoy, R.

“…We prove that every weak solution u to the 3D Navier–Stokes equation that belongs to the class L 3 L 9/2 and ∇ u belongs to L 3 L 9/5 locally away from a…”
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Operator algebras and the Fredholm spectrum of advective equations of linear hydrodynamics by Shvydkoy, R., Latushkin, Y.

“…In this paper we give a complete description of the Fredholm spectrum of the linearized 3D Euler equation in terms of the dynamical spectrum of the cocycle…”
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The largest linear space of operators satisfying the Daugavet equation in L_{1} by Shvydkoy, R. V.

“…We find the largest linear space of bounded linear operators on L_1(\Omega) that, being restricted to any L_1(A), A\subset \Omega , satisfy the Daugavet…”
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The Regularity of Weak Solutions of the 3D Navier-Stokes Equations in B^sub [INFINITY],[INFINITY]^^sup -1 by Cheskidov, A, Shvydkoy, R

“…We show that if a Leray-Hopf solution u of the three-dimensional Navier-Stokes equation belongs to C ( ( 0 , T ] ; B ∞ , ∞ − 1 ) or its jumps in the B ∞ , ∞ −…”
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The Regularity of Weak Solutions of the 3D Navier–Stokes Equations in by Cheskidov, A., Shvydkoy, R.

“…We show that if a Leray–Hopf solution u of the three-dimensional Navier–Stokes equation belongs to or its jumps in the -norm do not exceed a constant multiple…”
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The Regularity of Weak Solutions of the 3D Navier―Stokes Equations in B―1 by CHESKIDOV, A, SHVYDKOY, R, SVERAK, V

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Nonlinear instability for the navier-stokes equations by FRIEDLANDER, Susan, PAVLOVIC, Natasa, SHVYDKOY, Roman

“…It is proved, using a bootstrap argument, that linear instability implies nonlinear instability for the incompressible Navier-Stokes equations in Lp for all p…”
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Eulerian dynamics with a commutator forcing II: flocking by Shvydkoy, R, Tadmor, E

“…We continue our study of one-dimensional class of Euler equations, introduced in \cite{ST2016}, driven by a forcing with a commutator structure of the form…”
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The Unstable Spectrum of the Surface Quasi-Geostrophic Equation by Friedlander, Susan, Shvydkoy, Roman

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Essential Spectrum of the Linearized 2D Euler Equation and Lyapunov–Oseledets Exponents by Shvydkoy, Roman, Latushkin, Yuri

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Euler equations and turbulence: analytical approach to intermittency by Cheskidov, A, Shvydkoy, R

“…Physical models of intermittency in fully developed turbulence employ many phenomenological concepts such as active volume, region, eddy, energy accumulation…”
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Cocycles and Ma\~{n}e sequences with an application to ideal fluids by Shvydkoy, R

“…Journal of Differential Equations, 229/1 (2006), 49--62 Exponential dichotomy of a strongly continuous cocycle $\bFi$ is proved to be equivalent to existence…”
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Ill-posedness of basic equations of fluid dynamics in Besov spaces by Cheskidov, A, Shvydkoy, R

“…We give a construction of a divergence-free vector field $u_0 \in H^s \cap B^{-1}_{\infty,\infty}$, for all $s<1/2$, such that any Leray-Hopf solution to the…”
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