Submitted papers:
Series of three multi-disciplinary papers (around 170 pages total):
[99] D. Bresch, G. Narbona-Reina, A. Burgisser, M. Collombet. Mathematical topics in compressible flows from mono-phase systems to two-phase systems. Submitted Studies in Applied Maths (2023)
[100] D. Bresch, A. Burgisser, M. Collombet, G. Narbona-Reina. Two-Phase magma flows with phase exchanges – Part I – Physical modeling in a volcanic conduit. Submitted Studies in Applied Maths (2023)
[101] A. Burgisser, M. Collombet, G. Narbona-Reina, D. Bresch. Two-Phase magma flows with phase exchanges – Part II – 1.5D Numerical simulations of magma evolution in a volcanic conduit. Submitted in Applied Maths (2023).
CO-EDITIONS:
[1] Coéditeur avec E. Blayo et Li TaTsien d’un numéro spécial dans Ann. Math. Blaise Pascal (Volume 9, No2, 2002).
[2] Coéditeur avec T. Colin, M. Ghil et S. Wang d’un numéro spécial dans DCDS-Série A (Volume 11, 2004).
[3] Coéditeur avec B. Dimartino et F. Flori d’un numéro spécial dans Mathematical and Computer Modelling (2008).
[4] Coéditeur avec V. Calvez, E. Grenier et P. Vigneaux d’un numéro spécial dans ESAIM: Proc. Volume 30, August 2010. CEMRACS 2009: Mathematical Modelling in Medicine.
[5] Coéditeur avec P. Zhang d’un numéro spécial dans Science China Mathematics, Vol. 55, No. 2, (2012).
[6] Coéditeur avec Z.P. Xin d’un numéro spécial dans Methods Appl. Anal., Vol. 20, No. 2, (2013). Publication des interventions de 40 minutes de la session ”Etats de la Recherche” SMF: ”Topics on compressible Navier–Stokes equations”, (2012).
HANDBOOKS and ARTICLES in SPECIAL EDITIONS:
[1] D. Bresch. Shallow-water equations and related topics. Handbook of Dif- ferential Equations, Evolutionary equations, vol. 5, Edited by C.M. Dafermos and M. Pokorny ́, (2009), 1–102.
[2] E. Bonnetier, D. Bresch, V. Milisic. A priori convergence esti- mates for a rough Poisson-Dirichlet problem with natural vertical boundary conditions. Advances in Matematical Fluid Mecanics, Dedicated to Giovanni Paolo Galdi on the Occasion of his 60th Birthday (2009) A. Sequeira and R. Rannacher Editors, p.105-134.$
[3] D. Bresch, B. Desjardins, E. Grenier. Oscillatory limit with chang- ing eigenvalues: A formal study, p. 91–105. New Directions in Mathematical Fluid Mechanics. The Alexander V. Kazhikhov Memorial Volume. Series: Advances in Mathematical Fluid Mechanics. Fursikov, Andrei V.; Galdi, Giovanni P.; Pukhnachev, Vladislav V. (Eds.) (2010).
[4] D. Bresch, I. Ionescu, E. Fernandez-Nieto, P. Vigneaux. Aug- mented Lagrangian Method and Compressible Visco-Plastic Flows : Appli- cations to Shallow Dense Avalanches. p. 57–89. New Directions in Mathe- matical Fluid Mechanics The Alexander V. Kazhikhov Memorial Volume. Series: Advances in Mathematical Fluid Mechanics. Fursikov, Andrei V.; Galdi, Giovanni P.; Pukhnachev, Vladislav V. (Eds.) (2010).
[5] Co-auteur, avec R. Danchin, B. Desjardins, A. Novtony, M. Perepetlisa, d’un ouvrage dans Panoramas et synth`eses sur les fluides compressibles faisant suite aux cours de la session ” Etats de la Recherche” SMF: Topics on compressible Navier–Stokes equations, (2012) organized in Chambéry.
[6] D. Bresch, B. Desjardins. Weak solutions with density dependent viscosities. Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, Eds Y. Giga et A. Novotny (2017), Springer.
[7] D. Bresch, B. Desjardins, J.–M. Ghidaglia, E. Grenier, M. Hillairet. Multi-fluid Models Including Compressible Fluids. Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, Eds Y. Giga et A. Novotny (2017), Springer.
[8] D. Bresch, P.–E. Jabin. Quantitative regularity estimates for compressible transport equations New Trends and Results in Mathematical De- scription of Fluid Flows. Necas Center Series, 77–113. Eds M. Bulicek, E. Feireisl, M. Pokorny. Springer Nature Switzerland AG (2018).
[9] D. Bresch, P.–E. Jabin. Viscous compressible flows under pressure. Fluid under pressure, 105-148. Eds T. Bodnar, G.P. Galdi, S. Necasova. Birkhauser (2019).
[10] D. Bresch, C. Burtea, F. Lagoutière. Mathematical Justification of a Compressible Bifluid System with Different Pressure Laws: A Continuous Approach. Submitted Applicable Analysis – Special issue Homogenization in fluid mechanics and porous media (a tribute to the memory of Andro Mikelic), (2021).
This paper corresponds to the continuous approach explained in D. Bresch, C. Burtea, F. Lagoutière. Physical relaxation terms for compressible two-phase systems, see arXiv:2012.06497 The details of the semi-discrete approach with numerical simulations explained also in arXiv:2012.06497 is dedicated to a paper published in J. Comp. Phys (2023) (See the publications list).
[11] D. Bresch, R. Klein, X. Liu. The soundproof model of an acoustic-internal waves system with low stratification. J. Math Fluid Mech 24, Article number: 95 (2022). This is a paper in a collection dedicated to the memory of Antonin Novotny.
PROSPECTIVE DOCUMENTS AND SYNTHESIS:
+ With the help of E. Neveu:
[1] Synthèse de l’Atelier de Réflexion Prospective ANR (ARP) MathsInTerre, 2014 (16 pages).
[2] Document de restitution des travaux de l’Atelier de Réflexion Prospective ANR (ARP) MathsInTerre, 2014 (259 pages).
+ With the CNRS national committee for mathematics in 2019:
+ With a group of members of the LAMA UMR5127 CNRS in 2019:
[4] Charte éco-responsable du laboratoire.
+ With 6 colleagues: P. Biane, J. Barré, F. Hivert, E. Miot and S. Jaffard — E. Royer in 2023:
[5] Synthesis of working group 7 of the Assises des Mathématiques
.
Didier Bresch 