Publications of Roman Shvydkoy

A. Cheskidov and R. Shvydkoy.  Euler equations and turbulence: analytical approach to intermittency.  SIAM J. Math. Anal., 46(1):353--374, 2014. MR3152734
A. Cheskidov and R. Shvydkoy.  A unified approach to regularity problems for the 3D Navier-Stokes and Euler equations: the use of Kolmogorov's dissipation range.  J. Math. Fluid Mech., 16(2):263--273, 2014. MR3208714
Roman Shvydkoy.  A study of energy concentration and drain in incompressible fluids.  Nonlinearity, 26(2):425--436, 2013. MR3007898
Dongho Chae and Roman Shvydkoy.  On formation of a locally self-similar collapse in the incompressible Euler equations.  Arch. Ration. Mech. Anal., 209(3):999--1017, 2013. MR3067830
R. Shvydkoy.  A study of energy concentration and drain in incompressible fluids.  Nonlinearity 26 (2013) 425-436.  2013.
A. Cheskidov and R. Shvydkoy.  Ill-posedness for subcritical hyperdissipative Navier-Stokes equations in the largest critical spaces.  J. Math. Phys., 53(11):115620, 7, 2012. MR3026565
Alexey Cheskidov, Roman Shvydkoy and Susan Friedlander.  A continuous model for turbulent energy cascade.  In Mathematical aspects of fluid mechanics, pages 52--69.  Cambridge Univ. Press, Cambridge, 2012. MR3050291
R. Shvydkoy A. Cheskidov, S. Friedlander.  A continuous model for turbulent energy cascade.  London Mathematical Society Lecture Note Series (No. 402), Cambridge University Press, 2012, pp. 52-69.  2012.
Dongho Chae and Roman Shvydkoy.  On formation of a locally self-similar collapse in the incompressible Euler equations.  Archive for Rational Mechanics and Analysis, 20 pages.  2012.
A. Cheskidov and R. Shvydkoy.  Euler equations and turbulence: analytical approach to intermittency.  26 pages.  2012.
A. Cheskidov and R. Shvydkoy.  Ill-posedness for subcritical hyperdissipative Navier-Stokes equations in the largest critical spaces.  ournal of Mathematical Physics, 53/11, 2012, 115620-1–7.  2012.
R. Shvydkoy.  Convex integration for a class of active scalar equations.  J. Amer. Math. Soc., 24(4):1159--1174, 2011. MR2813340
A. Cheskidov and R. Shvydkoy.  Regularity problem for the 3D Navier-Stokes equations: the use of Kolmogorov's dissipation range.  2011.
A. Cheskidov and R. Shvydkoy.  The regularity of weak solutions of the 3D Navier-Stokes equations in $B^{-1}_{\infty,\infty}$.  Arch. Ration. Mech. Anal., 195(1):159--169, 2010. MR2564471
A. Cheskidov and R. Shvydkoy.  Ill-posedness of the basic equations of fluid dynamics in Besov spaces.  Proc. Amer. Math. Soc., 138(3):1059--1067, 2010. MR2566571
Roman Shvydkoy.  Lectures on the Onsager conjecture.  Discrete Contin. Dyn. Syst. Ser. S, 3(3):473--496, 2010. MR2660721
Miroslav Bul{\'{\i}}ček, Eduard Feireisl, Josef Málek and Roman Shvydkoy.  On the motion of incompressible inhomogeneous Euler-Korteweg fluids.  Discrete Contin. Dyn. Syst. Ser. S, 3(3):497--515, 2010. MR2660722
Alexey Cheskidov, Susan Friedlander and Roman Shvydkoy.  On the energy equality for weak solutions of the 3D Navier-Stokes equations.  In Advances in mathematical fluid mechanics, pages 171--175.  Springer, Berlin, 2010. MR2665030
Roman Shvydkoy.  Continuous spectrum of the 3D Euler equation is a solid annulus.  C. R. Math. Acad. Sci. Paris, 348(15-16):897--900, 2010. MR2677987
Roman Shvydkoy.  On the energy of inviscid singular flows.  J. Math. Anal. Appl., 349(2):583--595, 2009. MR2456214
R. Shvydkoy.  A geometric condition implying an energy equality for solutions of the 3D Navier-Stokes equation.  J. Dynam. Differential Equations, 21(1):117--125, 2009. MR2482010
R. Shvydkoy and Y. Latushkin.  Operator algebras and the Fredholm spectrum of advective equations of linear hydrodynamics.  J. Funct. Anal., 257(10):3309--3328, 2009. MR2568693
A. Cheskidov, P. Constantin, S. Friedlander and R. Shvydkoy.  Energy conservation and Onsager's conjecture for the Euler equations.  Nonlinearity, 21(6):1233--1252, 2008. MR2422377
Roman Shvydkoy and Susan Friedlander.  The unstable spectrum of the Navier-Stokes operator in the limit of vanishing viscosity.  Ann. Inst. H. Poincaré Anal. Non Linéaire, 25(4):713--724, 2008. MR2436790
Susan Friedlander, Nataša Pavlović and Roman Shvydkoy.  Nonlinear instability for the Navier-Stokes equations.  Comm. Math. Phys., 264(2):335--347, 2006. MR2215608
Roman Shvydkoy.  The essential spectrum of advective equations.  Comm. Math. Phys., 265(2):507--545, 2006. MR2231681
Roman Shvydkoy.  Cocycles and Mañe sequences with an application to ideal fluids.  J. Differential Equations, 229(1):49--62, 2006. MR2265617
Susan Friedlander and Roman Shvydkoy.  The unstable spectrum of the surface quasi-geostropic equation.  J. Math. Fluid Mech., 7(suppl. 1):S81--S93, 2005. MR2126131
Dmitriy Bilik, Vladimir Kadets, Roman Shvidkoy and Dirk Werner.  Narrow operators and the Daugavet property for ultraproducts.  Positivity, 9(1):45--62, 2005. MR2139116
Roman Shvydkoy and Susan Friedlander.  On recent developments in the spectral problem for the linearized Euler equation.  In Nonlinear partial differential equations and related analysis, pages 271--295.  Amer. Math. Soc., Providence, RI, 2005. MR2143872
Roman Shvydkoy and Yuri Latushkin.  Essential spectrum of the linearized 2D Euler equation and Lyapunov-Oseledets exponents.  J. Math. Fluid Mech., 7(2):164--178, 2005. MR2177125
Y. Charles Li and Roman Shvidkoy.  Isospectral theory of Euler equations.  J. Math. Anal. Appl., 292(1):311--315, 2004. MR2050234
Roman Shvydkoy and Misha Vishik.  On spectrum of the linearized 3D Euler equation.  Dyn. Partial Differ. Equ., 1(1):49--63, 2004. MR2091394
Roman Shvidkoy and Yuri Latushkin.  The essential spectrum of the linearized 2D Euler operator is a vertical band.  In Advances in differential equations and mathematical physics (Birmingham, AL, 2002), pages 299--304.  Amer. Math. Soc., Providence, RI, 2003. MR1991549
András Bátkai, Eva Fašanga and Roman Shvidkoy.  Hyperbolicity of delay equations via Fourier multipliers.  Acta Sci. Math. (Szeged), 69(1-2):131--145, 2003. MR1991661
Máté Matolcsi and Roman Shvidkoy.  Trotter's product formula for projections.  Arch. Math. (Basel), 81(3):309--317, 2003. MR2013262
B. Cascales and R. Shvydkoy.  On the Krein-\v Smulian theorem for weaker topologies.  Illinois J. Math., 47(4):957--976, 2003. MR2036985
R. V. Shvydkoy.  The largest linear space of operators satisfying the Daugavet equation in $L_ 1$.  Proc. Amer. Math. Soc., 130(3):773--777 (electronic), 2002. MR1866033
V. Kadets, B. Shumyatskiy, R. Shvidkoy, L. Tseytlin and K. Zheltukhin.  Some remarks on vector-valued integration.  Mat. Fiz. Anal. Geom., 9(1):48--65, 2002. MR1911073
Roman Shvidkoy.  A dimension-dependent maximal inequality.  Proc. Edinb. Math. Soc. (2), 45(3):547--548, 2002. MR1933736
Dmitriy Bilik, Vladimir Kadets, Roman Shvidkoy, Gleb Sirotkin and Dirk Werner.  Narrow operators on vector-valued sup-normed spaces.  Illinois J. Math., 46(2):421--441, 2002. MR1936927
Vladimir M. Kadets, Roman V. Shvidkoy and Dirk Werner.  Narrow operators and rich subspaces of Banach spaces with the Daugavet property.  Studia Math., 147(3):269--298, 2001. MR1853772
Yuri Latushkin and Roman Shvydkoy.  Hyperbolicity of semigroups and Fourier multipliers.  In Systems, approximation, singular integral operators, and related topics (Bordeaux, 2000), pages 341--363.  Birkhäuser, Basel, 2001. MR1882702
Vladimir M. Kadets, Roman V. Shvidkoy, Gleb G. Sirotkin and Dirk Werner.  Banach spaces with the Daugavet property.  Trans. Amer. Math. Soc., 352(2):855--873, 2000. MR1621757
R. V. Shvydkoy.  Geometric aspects of the Daugavet property.  J. Funct. Anal., 176(2):198--212, 2000. MR1784413
V. M. Kadets and R. V. Shvidkoy.  The Daugavet property for pairs of Banach spaces.  Mat. Fiz. Anal. Geom., 6(3-4):253--263, 1999. MR1737213
Vladimir M. Kadets, Roman V. Shvidkoy, Gleb G. Sirotkin and Dirk Werner.  Espaces de Banach ayant la propriété de Daugavet.  C. R. Acad. Sci. Paris Sér. I Math., 325(12):1291--1294, 1997. MR1490416
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