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Dissipative Euler flows for vortex sheet initial data without distinguished sign
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The Baire category method for intermittent convex integration
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2022
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Calculus of variations ; 14 August - 20 August 2022 ; report no. 37/2022
In: Oberwolfach reports, 19 (2022) 3, pp. 2129-2193inJournal
2022
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Global Nash-Kuiper theorem for compact manifolds
In: Journal of differential geometry, 122 (2022) 1, pp. 35-68inJournal
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Weak stability and closure in turbulence
In: Philosophical transactions of the Royal Society / A, 380 (2022) 2218, p. 20210091inJournal
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Nonexistence of \(T_4\) configurations for hyperbolic systems and the Liu entropy condition
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Non uniqueness of power-law flows
In: Communications in mathematical physics, 388 (2021) 1, pp. 199-243inJournal
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Non-uniqueness for the Euler equations up to Onsager's critical exponent
In: Annals of PDE, 7 (2021) 1, p. 8inJournal
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Bounded solutions of ideal MHD with compact support in space-time
In: Archive for rational mechanics and analysis, 239 (2021) 1, pp. 51-93Preprint
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Magnetic helicity, weak solutions and relaxation of ideal MHD
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A new approach to the Rayleigh-Taylor instability
In: Archive for rational mechanics and analysis, 241 (2021) 3, pp. 1243-1280inJournal
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Mixing solutions for the Muskat problem with variable speed
In: Journal of evolution equations, 21 (2021) 3, pp. 3289-3312inJournal
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Onsager's conjecture for admissible weak solutions
In: Communications on pure and applied mathematics, 72 (2019) 2, pp. 229-274inJournal
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\(C^{1,\alpha}\) isometric extensions
In: Communications in partial differential equations, 44 (2019) 7, pp. 613-636inJournal
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Very weak solutions to the two-dimensional Monge-Ampére equation
In: Science China mathematics, 62 (2019) 6, pp. 1041-1056inJournal
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On turbulence and geometry : from Nash to Onsager
In: Notices of the American Mathematical Society, 66 (2019) 5, pp. 677-685inJournal
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Non-renormalized solutions to the continuity equation
In: Calculus of variations and partial differential equations, 58 (2019) 6, p. 208inJournal
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Instabilities and non-uniqueness in ideal fluids [In: Mathematical aspects of hydrodynamics ; 18 August - 24 August 2019 ; report no. 38/2019]
In: Oberwolfach reports, 16 (2019) 3, pp. 2350-2351inJournal
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Instabilities and non-uniqueness in ideal fluids [In: Nonlinear hyperbolic problems : modeling, analysis, and numerics ; 19 May - 25 May 2019 ; report no. 24/2019]
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A Nash-Kuiper theorem for \(C^{1,\frac{1}{5}-\delta}\) immersions of surfaces in \(3\) dimensions
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\(T_5\)-configurations and non-rigid sets of matrices
In: Calculus of variations and partial differential equations, 57 (2018) 1, p. 19inJournal
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Piecewise constant subsolutions for the Muskat problem
In: Communications in mathematical physics, 363 (2018) 3, pp. 1051-1080inJournal
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Non-uniqueness for the transport equation with Sobolev vector fields
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Non-uniqueness and \(\mathscr h\)-principle for Hölder-continuous weak solutions of the Euler equations
In: Archive for rational mechanics and analysis, 224 (2017) 2, pp. 471-514inJournal
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High dimensionality and h-principle in PDE
In: Bulletin of the American Mathematical Society, 54 (2017) 2, pp. 247-282inJournal
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Laminates supported on cubes
In: Journal of convex analysis, 24 (2017) 4, pp. 1217-1237inJournal
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Dissipative Euler flows with Onsager-critical spatial regularity
In: Communications on pure and applied mathematics, 69 (2016) 9, pp. 1613-1670inJournal
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John Forbes Nash Jr. (1928-2015)
In: Notices of the American Mathematical Society, 63 (2016) 5, pp. 492-504inJournal
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Anomalous dissipation for 1/5-Hölder Euler flows
In: Annals of mathematics, 182 (2015) 1, pp. 127-172inJournal
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On \(\mathscr h\)-principle and Onsager's conjecture
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Equidimensional isometric maps
In: Commentarii mathematici Helvetici, 90 (2015) 4, pp. 761-798inJournal
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Non-uniqueness for the Euler equations : the effect of the boundary
In: Russian mathematical surveys, 69 (2014) 2, pp. 189-207inJournal
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Non-uniqueness for the Euler equations : the effect of the boundary
In: Uspechi matematiceskich nauk, 69 (2014) 2, pp. 3-22inJournal
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Weak solutions to the stationary incompressible Euler equations
In: SIAM journal on mathematical analysis, 46 (2014) 6, pp. 4060-4074inJournal
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Dissipative Euler flows and Onsager's conjecture
In: Journal of the European Mathematical Society, 16 (2014) 7, pp. 1467-1505inBook
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The \(\mathscr h\)-principle and turbulence
In: Proceedings of the international congress of mathematicians : August 13-21, 2014, Seoul, Korea ; Volume III - Invited lectures / Sun Young Jang... (eds.)Seoul : Kyung moon sa, 2014. - pp. 503-523
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Laminates meet Burkholder functions
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Transporting microstructure and dissipative Euler flows
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Continuous dissipative Euler flows and a conjecture of Onsager
In: Proceedings of the 6th european congress of mathematics, Kraków, Poland, July 2-7 July, 2012 / Rafał Latała (ed.)Zürich : European Mathematical Society, 2013. - pp. 13-29
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Dissipative continuous Euler flows
In: Inventiones mathematicae, 193 (2013) 2, pp. 377-407inBook
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From isometric embeddings to turbulence
In: HCDTE lecture notes. Part II. Nonlinear hyperbolic PDEs, dispersive and transport equations / Giovanni Alberti... (eds.)Springfield : American Institute of Mathematical Sciences, 2013. - pp. 195-255
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Uniqueness of normalized homeomorphic solutions to nonlinear Beltrami equations
In: International mathematics research notices, 2012 (2012) 18, pp. 4101-4119Preprint
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Dissipative continuous Euler flows in two and three dimensions
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\(\mathscr h\)-principle and rigidity for \(C^{1,a}\) isometric embeddings
In: Nonlinear partial differential equations : the Abel symposium 2010 ; proceedings of the Abel symposium, Oslo, Norway, September 28-October 2, 2010 / Helge Holden... (eds.)Berlin : Springer, 2012. - pp. 83-116
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The \(\mathscr h\)-principle and the equations of fluid dynamics
In: Bulletin of the American Mathematical Society, 49 (2012) 3, pp. 347-375inJournal
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Global solutions of the 2D Euler equations, starting with the work of Witold Wolibner
In: Roczniki Polskiego Towarzystwa Matematycznego = Annales Societatis Mathematicae Polonae. Seria 2, Wiadomosci matematyczne, 48 (2012) 2, pp. 257-269inJournal
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Relaxation of the incompressible porous media equation
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Young measures generated by ideal incompressible fluid flows
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The \(L^p\)-operator norm of a quadratic perturbation of the real part of the Ahlfors-Beurling operator
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Weak-strong uniqueness for measure-valued solutions
In: Communications in mathematical physics, 305 (2011) 2, pp. 351-361inJournal
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Weak solutions to the incompressible Euler equations with vortex sheet initial data
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On admissibility criteria for weak solutions of the Euler equations
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The Euler equations as a differential inclusion
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In: The interaction of analysis and geometry : international school-conference on analysis and geometry, Novosibirsk, Russia, August 23-September 3, 2004Providence, RI : American Mathematical Society, 2007. - pp. 227-245
(Contemporary mathematics ; 424)
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Erratum to: 'Rank-one convex hulls in \(\mathbb{R}^{2\times2}\)'
In: Calculus of variations and partial differential equations, 28 (2007) 4, pp. 545-546inJournal
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Simple proof of two-well rigidity
In: Comptes rendus mathematique, 343 (2006) 5, pp. 367-370inJournal
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On quasiconvex hulls in symmetric \(2\times 2\) matrices
In: Annales de l'Institut Henri Poincaré / C, 23 (2006) 6, pp. 865-876inJournal
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On the local structure of rank-one convex hulls
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Rank-one convex hulls in \(\mathbb{R}^{2\times2}\)
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Elliptic regularity versus rank-one convexity
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