Onsager's Conjecture with Physical Boundaries and an Application to the Vanishing Viscosity Limit

J. Leray, Sur le mouvement d’un liquide visqueux emplissant l’espace (French), Acta Math

1934

Earlier work this paper cites.

L. Onsager, Statistical hydrodynamics, Nuovo Cimento

1949

Earlier work this paper cites.

L. Schwartz, Théorie des Distributions (French). Publications de l’Institut de Mathématique de l’Université de Strasbourg, No. IX-X. Hermann, Paris

1966

Earlier work this paper cites.

R. Temam, On the Euler equations of incompressible perfect fluids, J. Functional Analysis

1975

Earlier work this paper cites.

T. Kato, Remarks on on zero viscosity limit for nonstationary Navier-Stokes flows with boundary, Seminar on Nonlinear Partial Differential Equations (Berkeley, Calif., 1983), Math. Sci. Res. Inst. Publ.,

1984

Earlier work this paper cites.

M. Germano, Differential filters of elliptic type, Phys. Fluids

1986

Earlier work this paper cites.

P. Constantin, W. E, and E.S. Titi, Onsager’s Conjecture on the energy conservation for solutions of Euler’s equation, Comm. Math. Phys

1994

Earlier work this paper cites.

G. L. Eyink, Energy dissipation without viscosity in ideal hydrodynamics, I. Fourier analysis and local energy transfer, Phys. D

1994

Earlier work this paper cites.

N. V. Krylov, Lectures on Elliptic and Parabolic Equations in Hölder Spaces. Graduate Studies in Mathematics, 12. American Mathematical Society

1996

Earlier work this paper cites.

S. Chen, C. Foias, D. Holm, E. Olson, E. S. Titi and S. Wynne, A connection between Camassa–Holm equations and turbulent flows in channels and pipes, Physics of Fluids

1999

Earlier work this paper cites.

S. Chen, C. Foias, D. Holm, E. Olson, E. S. Titi and S. Wynne, The Camassa–Holm equations and turbulence, Physica D

1999

Cited alongside, same era.

J. Duchon and R. Robert, Inertial energy dissipation for weak solutions of incompressible Euler and Navier-Stokes equations, Nonlinearity

2000

Cited alongside, same era.

A. Cheskidov, D. D. Holm, E. Olson, and E. S. Titi, On a Leray- α \alpha model of turbulence, Royal Society London, Proceedings, Series A, Mathematical, Physical & Engineering Sciences

2005

Cited alongside, same era.

A. A. Ilyin, E. M. Lunasin and E.S. Titi, A modified-Leray − α -\alpha subgrid scale model of turbulence, Nonlinearity

2006

Cited alongside, same era.

A. Cheskidov, P. Constantin, S. Friedlander, and R. Shvydkoy, Energy conservation and Onsager’s conjecture for the Euler equations, Nonlinearity

2008

C. Yu, Energy conservation for the weak solutions of the compressible Navier-Stokes equations, Arch. Ration. Mech. Anal

2017

Later among the works it cites.

C. Bardos, P. Gwiazda, A. Świerczewska-Gwiazda, E.S. Titi and E. Wiedemann, On the extension of Onsager’s conjecture for general conservation laws, Journal of Nonlinear Science

2018

Closest in time.

C. Bardos and E. S. Titi, Onsager’s Conjecture for the incompressible Euler equations in bounded domains, Arch. Ration. Mech. Anal

2018

Closest in time.

P. Constantin and V. Vicol, Remarks on high Reynolds numbers hydrodynamics and the inviscid limit, Journal of Nonlinear Science

2018

Closest in time.

T. D. Drivas and G. L. Eyink, An Onsager singularity theorem for turbulent solutions of compressible Euler equations, Comm. Math. Phys

2018

Closest in time.