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We consider active scalar equations $\partial_t \theta + \nabla \cdot (u \, \theta) = 0$, where $u = T[\theta]$ is a divergence-free velocity field, and $T$ is a Fourier multiplier operator with symbol $m$.
The local structure of turbulence in an incompressible viscous fluid
A. N. Kolmogorov · 1941
Earlier work this paper cites.
Statistical hydrodynamics
L. Onsager · 1949
Earlier work this paper cites.
C 1 {C}^{1} isometric embeddings i, ii
J. Nash · 1954
Earlier work this paper cites.
Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l’hydrodynamique des fluides parfaits
V. Arnold · 1966
Earlier work this paper cites.
Small-scale structure of a scalar field convected by turbulence
R.H. Kraichnan · 1968
Earlier work this paper cites.
Dynamics of fluids in porous media
J. Bear · 1972
Earlier work this paper cites.
Navier–stokes equations
P. Constantin and C. Foias · 1988
Earlier work this paper cites.
Onsager’s conjecture on the energy conservation for solutions of Euler’s equation
P. Constantin, W. E, and E.S. Titi · 1994
Earlier work this paper cites.
Formation of strong fronts in the 2 2 -D quasigeostrophic thermal active scalar
P. Constantin, A.J. Majda, and E. Tabak · 1994
Earlier work this paper cites.
The magnetostrophic rise of a buoyant parcel in the earth’s core
H.K. Moffatt and D.E. Loper · 1994
Earlier work this paper cites.
Surface quasi-geostrophic dynamics
I.M. Held, R.T. Pierrehumbert, S.T. Garner, and K.L. Swanson · 1995
Earlier work this paper cites.
Dynamical problems in non-linear advective partial differential equations
S.G. Resnick · 1995
Earlier work this paper cites.
Scaling exponents for active scalars
P. Constantin · 1998
Earlier work this paper cites.
Energy spectrum of quasigeostrophic turbulence
P. Constantin · 2002
Earlier work this paper cites.
Studying Nonlinear PDE by geometry in matrix space
B. Kirchheim, S. Müller, and V. Šverák · 2003
Earlier work this paper cites.
Contour dynamics of incompressible 3-D fluids in a porous medium with different densities
D. Córdoba and F. Gancedo · 2007
Earlier work this paper cites.
Analytical behavior of two-dimensional incompressible flow in porous media
D. Córdoba, F. Gancedo, and R. Orive · 2007
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Energy conservation and Onsager’s conjecture for the Euler equations
A. Cheskidov, P. Constantin, S. Friedlander, and R. Shvydkoy · 2008
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Magnetostrophic turbulence and the geodynamo
H.K. Moffatt · 2008
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The Euler equations as a differential inclusion
C. De Lellis and L. Székelyhidi, Jr · 2009
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h-principle and rigidity for C 1 , α {C}^{1,\alpha} isometric embeddings. To appear in
S. Conti, C. De Lellis, and L. Székelyhidi, Jr · 2010
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Lectures on the Onsager conjecture
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On a singular incompressible porous media equation
S. Friedlander, F. Gancedo, W. Sun, and V. Vicol · 2012
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Hölder continuous Euler flows in three dimensions with compact support in time
P. Isett · 2012
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Relaxation of the incompressible porous media equation
L. Székelyhidi Jr · 2012
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Non-uniqueness for the euler equations: the effect of the boundary
C. Bardos, L. Székelyhidi Jr, and E. Wiedemann · 2013
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Mathematics and turbulence: where do we stand?
C. Bardos and E.S. Titi · 2013
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