L. Ambrosio, Transport equation and Cauchy problem for BV vector fields, Invent. math, pp.227-260, 2004.
DOI : 10.1007/s00222-004-0367-2

L. Ambrosio and G. Crippa, Existence, Uniqueness, Stability and Differentiability Properties of the Flow Associated to Weakly Differentiable Vector Fields, Lect. Notes Unione Mat. Ital, vol.5, 2008.
DOI : 10.1007/978-3-540-76781-7_1

H. Beirão and . Veiga, A new regularity class for the Navier-Stokes equations in R n , Chinese Annals Math, pp.407-412, 1995.

F. Bouchut and F. James, One-dimensional transport equations with discontinuous coefficients, Nonlinear Analysis, Theory, Methods and Applications, pp.891-933, 1998.
DOI : 10.1016/s0362-546x(97)00536-1

URL : http://www.labomath.univ-orleans.fr/~james/Postscripts/dualpap.ps

F. Bouchut and F. James, Duality solutions for pressureless gases, monotone scalar conservation laws, and uniqueness Comm, Partial Diff. Eq, vol.24, pp.11-12, 1999.

F. Bouchut, F. James, and S. Mancini, Uniqueness and weak stability for multidimensional transport equations with one-sided Lipschitz coefficients, Ann. Scuola Norm. Sup. Pisa Cl. Sci, issue.5, pp.1-25, 2005.

T. Buckmaster, C. De-lellis, L. Székelyhidi, and V. Vicol, Onsager's conjecture for admissible weak solutions

L. Caffarelli, R. Kohn, and L. Nirenberg, Partial regularity of suitable weak solutions of the navier-stokes equations, Communications on Pure and Applied Mathematics, vol.8, issue.6, pp.771-831, 1982.
DOI : 10.1090/trans2/065/03

J. Chemin and P. Zhang, On the critical one component regularity for the 3D Navier-Stokes equations, Ann. sci. de l'ENS, vol.49, issue.1, pp.131-167, 2016.

G. Crippa and S. Spirito, Renormalized Solutions of the 2D Euler Equations, Communications in Mathematical Physics, vol.179, issue.3, p.339, 2015.
DOI : 10.1007/s00205-005-0390-5

C. De-lellis and L. Székelyhidi, On Admissibility Criteria for Weak Solutions of the Euler Equations, Archive for Rational Mechanics and Analysis, vol.136, issue.3, pp.225-260, 2010.
DOI : 10.1007/978-3-642-56200-6_1

N. Depauw, Non unicit?? des solutions born??es pour un champ de vecteurs BV en dehors d'un hyperplan, Comptes Rendus Mathematique, vol.337, issue.4, pp.249-252, 2003.
DOI : 10.1016/S1631-073X(03)00330-3

R. J. Diperna and P. , Lions, Ordinary differential equations, transport theory and Sobolev spaces, Invent. math, pp.511-547, 1989.

E. Fabes, B. Jones, and N. M. Riviere, The initial value problem for the Navier-Stokes equations with data in L p , Archive Rational Mechanics Analysis 45, pp.222-248, 1972.

C. Fabre and G. Lebeau, R??GULARIT?? ET UNICIT?? POUR LE PROBL??ME DE STOKES, Communications in Partial Differential Equations, vol.29, issue.1, pp.437-475, 2002.
DOI : 10.1137/S0036144598334588

Y. Giga, Solutions for semilinear parabolic equations in Lp and regularity of weak solutions of the Navier-Stokes system, Journal of Differential Equations, vol.62, issue.2, pp.186-212, 1986.
DOI : 10.1016/0022-0396(86)90096-3

J. Guillod and V. Sverák, Numerical investigations of non-uniqueness for the Navier?Stokes initial value problem in borderline spaces

P. Isett, A Proof of Onsager's Conjecture, 2016.

L. Bris and P. Lions, Existence and Uniqueness of Solutions to Fokker???Planck Type Equations with Irregular Coefficients, Communications in Partial Differential Equations, vol.83, issue.7, pp.1272-1317, 2008.
DOI : 10.1090/S0002-9904-1977-14312-7

URL : https://hal.archives-ouvertes.fr/hal-00667315

P. , L. Floch, and Z. Xin, Uniqueness via the adjoint problems for systems of conservation laws, Comm. on Pure and Applied Maths., XLVI, issue.11, pp.1499-1533, 1993.

J. Leray, Sur le mouvement d'un liquide visqueux emplissant l'espace, Acta Mathematica, vol.63, issue.0, pp.193-248, 1934.
DOI : 10.1007/BF02547354

URL : http://doi.org/10.1007/bf02547354

N. Lerner, Transport equations with partially BV velocities, Ann. Sc. Norm. Super. Pisa Cl. Sci, vol.3, issue.4, pp.681-703, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00021015

G. Lévy, On uniqueness for a rough transport???diffusion equation, Comptes Rendus Mathematique, vol.354, issue.8, pp.804-807, 2016.
DOI : 10.1016/j.crma.2016.05.003

V. Scheffer, An inviscid flow with compact support in space-time, Journal of Geometric Analysis, vol.110, issue.4, pp.343-401, 1993.
DOI : 10.1007/BF01205547

A. Shnirelman, On the nonuniqueness of weak solution of the Euler equation, Communications on Pure and Applied Mathematics, vol.50, issue.12, pp.1261-1286, 1997.
DOI : 10.1002/(SICI)1097-0312(199712)50:12<1261::AID-CPA3>3.0.CO;2-6

A. Shnirelman, Weak Solutions with Decreasing Energy??of Incompressible Euler Equations, Communications in Mathematical Physics, vol.210, issue.3, pp.541-603, 2000.
DOI : 10.1007/s002200050791

J. Serrin, On the interior regularity of weak solutions of the Navier-Stokes equations, Archive for Rational Mechanics and Analysis, vol.9, issue.1, pp.187-195, 1962.
DOI : 10.1007/BF00253344

M. Struwe, On partial regularity results for the navier-stokes equations, Communications on Pure and Applied Mathematics, vol.62, issue.4, pp.437-458, 1988.
DOI : 10.1007/978-3-663-13911-9

E. Tadmor, On a new scale of regularity spaces with applications to Euler's equations, Nonlinearity, vol.14, issue.3, 2001.
DOI : 10.1088/0951-7715/14/3/305

T. Tao, Finite time blowup for an averaged three-dimensional Navier-Stokes equation, Journal of the American Mathematical Society, vol.29, issue.3, pp.601-674, 2016.
DOI : 10.1090/jams/838

URL : http://arxiv.org/pdf/1402.0290

W. Wahl, Regularity of weak solutions of the Navier-Stokes equations, Proc. Symp. Pure Math, pp.497-503, 1986.