Publications

Introductory and review papers

Book

Proceedings

  • R. Danchin: Poches de tourbillon visqueuses, Séminaire EDP de l'Ecole Polytechnique, exposé IX (1995-96).

  • R. Danchin: Evolution d'une singularité de type cusp dans une poche de tourbillon, Journées EDP de Saint-Jean-de-Monts, 1997.

  • R. Danchin: Existence globale dans des espaces critiques pour le système de Navier-Stokes compressible, Séminaire EDP de l'Ecole Polytechnique, exposé XXI (1998-99).

  • R. Danchin: Evolution of a cusp-like singularity in a vortex patch, International Series of Numerical Mathematics, 129, pages 189-194 (1999).

  • R. Danchin : Fluides légèrement compressibles et limite incompressible, Séminaire EDP de l'Ecole Polytechnique, exposé III (2000-01).

  • J. Ben Ameur, R. Danchin: Limite non visqueuse pour les fluides incompressibles axisymétriques, Nonlinear partial differential equations and their applications, Vol. 14, Studies in Mathematics and its Applications, 31 , pages 29-55 (2002).

  • R. Danchin: Fluides incompressibles à densité variable, Séminaire équations aux Dérivées Partielles, Exp. No. XI, Palaiseau, 2002-2003.

  • R. Danchin: Navier-Stokes equations with variable density, Hyperbolic Problems and Related Topics, International Press, Graduate Series in Analysis, pages 121-135 (2003).

  • S. Benzoni-Gavage, R. Danchin, S. Descombes and D. Jamet: On Korteweg models for fluids exhibiting phase changes, Proceedings of the Tenth International Conference on Hyperbolic Problems, Kyoto (2004).

  • S. Benzoni-Gavage, R. Danchin, S. Descombes et D. Jamet: Stability issues in the Euler-Korteweg model, Contemporary Mathematics, Proceedings of the Summer Research Conference on Control Methods in PDE-Dynamical Systems, Snowbird (2005). A.M.S. 426, pages 103-127 (2007).

  • F. Bethuel, R. Danchin, P. Gravejat, J.-C. Saut et D. Smets: Les équations d'Euler, des ondes et de Korteweg-de Vries comme limites asymptotiques de l'équation de Gross-Pitaevskii, exposé I (2008-09).

  • R. Danchin and P.B. Mucha: Problème de Stokes et système de Navier-Stokes incompressible à densité variable dans le demi-espace, Séminaire EDP de l'Ecole Polytechnique, exposé X, (2008-09).

  • R. Danchin and P.B. Mucha: New maximal regularity results for the heat equation in exterior domains, and applications. Studies in phase space analysis with applications to PDEs, 101-128, Progr. Nonlinear Differential Equations Appl., 84, Birkhauser/Springer, New York, 2013.

  • R. Danchin et B. Ducomet: Résultats d'existence globale et limites asymptotiques pour un modèle de fluide radiatif. Séminaire EDP de l'Ecole Polytechnique, exposé VI, (2014-15).

Research papers

Incompressible homogeneous flows

  • R. Danchin : Poches de tourbillon visqueuses, Notes aux CRAS, 323, série 1, pages 147-150 (1996).

  • R. Danchin: Poches de tourbillon visqueuses, Journal de Mathématiques Pures et Appliquées, 76, pages 609-647 (1997).

  • R. Danchin: Evolution temporelle d'une poche de tourbillon singulière, Communication in Partial Differential Equations, 22, pages 685-721 (1997).

  • R. Danchin: Persistance de structures géométriques et limite non visqueuse pour les fluides incompressibles en dimension quelconque, Bulletin de la Société Mathématique de France, 127, pages 179-227 (1999).

  • A. Cohen and R. Danchin: Multiscale approximation of vortex patches, SIAM Journal on Applied Mathematics, 60, pages 477-502.

  • R. Danchin: Evolution d'une singularité de type cusp dans une poche de tourbillon, Revista Matemática Iberoamericana, 16, pages 281-329 (2000).

  • H. Abidi, R. Danchin: Optimal bounds for the inviscid limit of Navier-Stokes equations, Asymptotic analysis, 38 , pages 35-46 (2004).

  • R. Danchin: On perfect fluids with bounded vorticity, Notes aux CRAS, 345, pages 391-394 (2007).

  • R. Danchin: Axisymmetric incompressible flows with bounded vorticity, Russian Mathematical Surveys, 62, pages 73-94 (2007).

  • R. Danchin and M. Paicu: le théorème de Leray et le théorème de Fujita-Kato pour le système de Boussinesq partiellement visqueux, Bulletin de la SMF, 136(2), pages 261-309 (2008).

  • R. Danchin and M. Paicu: Existence and uniqueness results for the Boussinesq system with data in Lorentz spaces, Physica D, 237, pages 1444-1460 (2008).

  • R. Danchin and M. Paicu: Global well-posedness issues for the inviscid Boussinesq system with Yudovich's type data, Communications in Mathematical Physics, 290, pages 1-14 (2009).

  • R. Danchin and M. Paicu: Global existence results for the anisotropic Boussinesq system in dimension two, Math. Models Methods Appl. Sci, 21(3), 421-457 (2011).

  • R. Danchin: Remarks on the lifespan of the solutions to some models of incompressible fluid mechanics, Proc. Amer. Math. Soc., 141(6), 1979-1993 (2013).

  • R. Danchin and X. Zhang: Global persistence of geometrical structures for the Boussinesq equation with no diffusion, Communications in Partial Differential Equations, 42(1), 68-99 (2017).

Incompressible inhomogeneous flows

  • R. Danchin: Density-dependent incompressible fluids in critical spaces, Proceedings of the Royal Society of Edinburgh, 133, pages 1311-1334 (2003).

  • R. Danchin: Local and global well-posedness results for flows of inhomogeneous viscous fluids, Advances in Differential Equations, 9, pages 353-386 (2004).

  • R. Danchin: The inviscid limit for density-dependent incompressible fluids, Journal de la faculté de Sciences de Toulouse, 15, pages 637-688 (2006).

  • R. Danchin Density dependent incompressible fluids in bounded domains, Journal of Mathematical Fluid Mechanics, 8, pages 333-381 (2006).

  • R. Danchin and P. B. Mucha: A critical functional framework for the inhomogeneous Navier-Stokes equations in the half-space, Journal of Functional Analysis, 256(3), pages 881-927 (2009).

  • R. Danchin: On the well-posedness of the incompressible density-dependent Euler equations in the L^p framework. Journal of Differential Equations, 248, 2130-2170 (2010).

  • R. Danchin and F. Fanelli: The well-posedness issue for the density-dependent Euler equations in endpoint Besov spaces, J. Math. Pures Appl., 96, 253-278 (2011).

  • R. Danchin and P.B. Mucha: A Lagrangian approach for the incompressible Navier-Stokes equations with variable density, Communications on Pure and Applied Mathematics, 65(10), 1458-1480 (2012).

  • R. Danchin and X. Liao: On the well-posedness of the full low Mach number limit system in general critical Besov spaces, Comm. Contemp. Math., 14(3), 1250022, 47 pp.

  • R. Danchin and P.B. Mucha: Incompressible flows with piecewise constant density, Arch. Ration. Mech. Anal., 207(3), 991-1023 (2013)

  • R. Danchin and P. Zhang: Inhomogeneous Navier-Stokes equations in the half-space, with only bounded density, J. Funct. Anal., 267(7), 2371-2436 (2014).

  • R. Danchin and P.B. Mucha: Critical functional framework and maximal regularity in action on systems of incompressible flows, Mémoires de la SMF, 143, 151 pages (2015).

  • R. Danchin and X. Zhang: On the persistence of Hölder regular patches of density for the inhomogeneous Navier-Stokes equations, Journal de l'Ecole Polytechnique, 4, 781-811 (2017).

  • R. Danchin and P.B. Mucha: The Navier-Stokes equations in vacuum, Communications on Pure and Applied Mathematics, 72, pages 1351-1385 (2019).

Compressible Navier-Stokes equations

  • R: Danchin: Existence globale dans les espaces critiques pour le système de Navier-Stokes compressible, Comptes Rendus de l'Académie des Sciences, Paris, Série I, 328, pages 649-652 (1999).

  • R: Danchin: Global existence in critical spaces for compressible Navier-Stokes equations, Inventiones Mathematicae, 141, pages 579-614 (2000).

  • R: Danchin: Global existence in critical spaces for compressible viscous and heat conductive gases, Archive for Rational Mechanics and Analysis, 160, pages 1-39 (2001).

  • R: Danchin: Local theory in critical spaces for compressible viscous and heat conductive gases, Communications in Partial Differential Equations, 26, pages 1183-1233 (2001).

  • R: Danchin: Zero Mach number limit in critical spaces for compressible Navier-Stokes equations, Annales Scientifiques de l'Ecole Normale Supérieure, 35, pages 27-75 (2002).

  • R: Danchin: Zero Mach number limit in critical spaces for compressible flows with periodic boundary conditions, American Journal of Mathematics, 124, pages 1153-1219 (2002).

  • R: Danchin: On the uniqueness in critical spaces for compressible Navier-Stokes equations, Nonlinear Differential Equations and Applications, 12, pages 111-128 (2005).

  • R. Danchin: Well-posedness in critical spaces for barotropic viscous fluids with truly non constant density, Communications in Partial Differential Equations, 32, pages 1373-1397 (2007).

  • R. Danchin : On the solvability of the compressible Navier-Stokes system in bounded domains, Nonlinearity, 23(2), pages 383-408 (2010).

  • F. Charve and R. Danchin: A global existence result for the compressible Navier-Stokes equations in the critical Lp framework, Archive for Rational Mechanics and Analysis, 198(1), pages 233-271 (2010).

  • R. Danchin and L. He: The Oberbeck-Boussinesq approximation in critical spaces, Asymptotic analysis, 84, 61-102 (2013).

  • R. Danchin and B. Ducomet: On a simplified model for radiating flows, J. Evol. Equ., 14(1), 155-195 (2014).

  • R. Danchin: A Lagrangian approach for the compressible Navier-Stokes equations, Annales de l'Institut Fourier, 64(2), pages 753-791 (2014).

  • N. Chikami and R. Danchin: On the well-posedness of the full compressible Navier-Stokes system in critical Besov spaces, Journal of Differential Equations, 258(10), 3435-3467 (2015).

  • R. Danchin and L. He: The incompressible limit in Lp type critical spaces, Mathematische Annalen, 366(3-4), 1365-1402 (2016).

  • R. Danchin and B. Ducomet: The low Mach number limit for a barotropic model of radiative flow, SIAM J. on Math. Analysis, 48(2), 1025-1053 (2016).

  • R. Danchin and B. Ducomet: Diffusive limits for a barotropic model of radiative flows, Confluentes Mathematici, 8(1), 31-87 (2016).

  • R. Danchin and B. Ducomet: Existence of strong solutions with critical regularity to a polytropic model for radiating flows, Annali di Matematica Pura ed Applicata, 196(1), 107-153 (2017).

  • R. Danchin and J. Xu: Optimal time-decay estimates for the compressible Navier-Stokes equations in the critical L^p framework, Archive for Rational Mechanics and Analysis, 224(1), 53-90 (2017).

  • N. Chikami and R. Danchin: On the global existence and time decay estimates in critical spaces for the Navier-Stokes-Poisson system, Mathematische Nachrichten, 290(13), pages 1939-1970 (2017).

  • R. Danchin and P.B. Mucha: Compressible Navier-Stokes equations : large solutions and incompressible limit, Advances in Mathematics, 320, 904-925 (2017).

  • R. Danchin and P.B. Mucha: From compressible to incompressible inhomogeneous flows in the case of large data, Tunisian Journal of Mathematics, 1, pages 127-149 (2019).

  • R. Danchin and J. Xu: Optimal decay estimates in the critical L^p framework for flows of compressible viscous and heat-conductive gases, Journal of Mathematical Fluid Mechanics, 20, pages 1641-1665 (2018).

  • R. Danchin, F. Fanelli and M. Paicu: A well-posedness result for viscous compressible fluids with only bounded density, Analysis and PDEs, 13, pages 275-316 (2020).

  • R. Danchin, P. Mucha and P. Tolksdorf: Lorentz spaces in action on pressureless systems arising from models of collective behavior, Journal of Evolution Equations, 21, 3103-3127 (2021).

  • R. Danchin and P.B. Mucha: Compressible Navier-Stokes equations with ripped density, Communications on Pure and Applied Mathematics, to appear.

Compressible models with capillarity

Miscellaneous

  • R. Danchin: A few remarks on Camassa-Holm equation, Differential and Integral Equations, 14, pages 953-988 (2001).

  • R. Danchin: A note on well-posedness for Camassa-Holm equation, Journal of Differential Equations, 192, pages 429-444 (2003).

  • R. Danchin: Estimates in Besov spaces for transport and transport-diffusion equations with almost Lipschitz coefficients, Revista Matemática Iberoamericana, 21, pages 861-886 (2005).

  • R. Danchin : Uniform estimates for transport-diffusion equations, Journal of Hyperbolic Differential Equations, 4, pages 1-17 (2007).

  • F. Bethuel, R. Danchin and D. Smets : On the linear wave regime of the Gross-Pitaevskii equation, Journal d'Analyse Mathématique, 110(1), pages 297-338 (2010).

  • R. Danchin and P.B. Mucha: The divergence equation in rough spaces, J. Math. Anal. Appl. 386(1), 9-31 (2012).

  • R. Danchin and P.B. Mucha: Divergence, Discrete Contin. Dyn. Syst. Ser. S, 6, 1163-1172 (2013).

  • H. Bahouri, J.-Y. Chemin and R. Danchin: A frequency space for the Heisenberg group, Annales de l'Institut Fourier, 69, pages 365-407 (2019).

  • H. Bahouri, J.-Y. Chemin and R. Danchin: Tempered distributions and Fourier transform on the Heisenberg group, Annales de lĂ•Institut Henri Lebesgue, 1, pages 1-46 (2018).

  • R. Danchin, P.B. Mucha, J. Peszek and B. Wróblewski: Regular solutions to the fractional Euler alignment system in the Besov spaces framework, Math. Models Methods Appl. Sci., 29, pages 89-119 (2019).

  • X. Blanc, R. Danchin, B. Ducomet and S. Necasova: The global existence issue for the compressible Euler system with Poisson or Helmholtz couplings. J. Hyperbolic Differ. Equ., 18(1), pages 169-193 (2021).

  • R. Danchin and J. Tan: On the well-posedness of the Hall-magnetohydrodynamics system in critical spaces, Communications in Partial Differential Equations, 46(1), pages 31-65 (2021).

  • R. Danchin, B. Ducomet: On the global existence for the compressible Euler-Poisson system, and the instability of static solutions, Journal of Evolution Equations, 21, pages 3035-3054 (2021).

  • R. Danchin, B. Ducomet: On the global existence for the compressible Euler-Riesz system, Journal of Mathematical Fluid Mechanics, 24, Paper No. 48, 25 pp (2022).

  • R. Danchin and J. Tan: The global solvability of the Hall-Magnetodhydrodynamics system in critical Sobolev spaces, Communications in Contempory Mathematics, to appear.

  • T. Crin-Barat and R. Danchin: Partially dissipative one-dimensional hyperbolic systems in the critical regularity setting, and applications, Pure and Applied Analysis, 4, pages 85-125 (2022).

  • T. Crin-Barat and R. Danchin: Partially dissipative hyperbolic systems in the critical regularity setting: The multi-dimensional case, Journal de Mathématiques Pures et Appliquée, 165, pages 1-41 (2022).

  • T. Crin-Barat and R. Danchin: Partially dissipative systems in the critical regularity setting, and strong relaxation limit, Mathematische Annalen, to appear.