Publications 2001-2010

[8] D. Bresch, J. Lemoine, J. Simon. A geostrophic model with verti- cal diffusion. Nonlinear Analysis, Theory, Methods and Applications, 43/4, (2001), 449–470.

[9] D. Bresch, J. Simon. On the effect of friction on wind driven shallow lakes, J. Math. Fluid Mech. (2001), 231–258.

[10] Y. Amirat, D. Bresch, J. Lemoine, J. Simon. Effect of rugosity on a flow governed by Navier–Stokes equations. Quarterly Appl. Math, 59, no. 4, (2001), 769–785.

[11] D. Bresch, B. Desjardins, E. Grenier, C.K. Lin. Low Mach Number Limit of Viscous Polytropic Flows: Formal Asymptotics in the Pe- riodic Case, Studies Applied Math., 109, (2002), 125–148.

[12] D. Bresch, T. Colin. Some remarks on the derivation of the Sverdrup relation, J. Math. Fluid Mech. 4, 2, (2002), 95–108.

[13] D. Bresch, T. Huck, M. Sy. Circulation thermohaline et équations planétaires géostrophiques: propriétés physiques, numériques et mathématiques, Ann. Math. Blaise Pascal, 9, No2, (2002), 181–212.

[14] D. Bresch, F. Guillen-Gonzalez, N. Masmoudi, M.A. Rodriguez- Bellido. On the uniqueness of weak solutions of the two-dimensional prim- itive equations, Diff. and Int. Eqs, 16, Number 1, (2003), 77–94.

[15] D. Bresch, F. Guillen-Gonzalez, N. Masmoudi, M.A. Rodriguez- Bellido. Asymptotic derivation of a Navier condition for the Primitive equations, Asymptotic Analysis, 33, (2003), 237–259.

[16] D. Bresch, J. Simon. Western boundary currents versus vanishing depth, Discrete and continuous dynamical systems-Series B, 3, (2003), 469– 477.

[17] D. Bresch, M. Sy. Porous convection in rotating thin domains: the planetary geostrophic equations, used in geophysical fluid dynamics, revis- ited, Cont. Mech. Thermodyn. 15 (2003) 3, 247–263.

[18] D. Bresch, B. Desjardins, C.K. Lin. On some compressible fluid models: Korteweg, lubrication and shallow water systems, Comm. Part. Diff. Eqs. 28, 3–4, (2003), 1009–1037.

[19] D. Bresch, B. Desjardins. Existence of global weak solutions for a 2D viscous shallow water equations and convergence to the quasi-geostrophic model, Commun. Math. Phys. 238 (2003) 1-2, 211–223. Extension de : D. Bresch, B. Desjardins. Sur un modèle de Saint-Venant visqueux et sa limite quasi-géostrophique, C. R. Acad. Sci. Paris, 335, S ́erie I, (2002), 1079–1084.

[20] D. Bresch. A direct asymptotic analysis on a nonlinear model with thin layers, Ann. Univ. Ferrara, Sez VII, Sc. Mat., vol. II, (2003), 359–373.

[21] D. Bresch, F. Guillén-Gonzalez, M.A. Rodriguez-Bellido. A corrector for the Sverdrup solution for a domain with islands, Applicable Anal. 83 (2004), 3, 217–230.

[22] D. Bresch, B. Desjardins, D. Gérard-Varet. Rotating fluids in a cylinder, numéro spécial ”Some Evolution Equations and their Qualitative Properties”, Série DCDS Série A, Vol. 11, Number 1, 47–82, (2004).

[23] D. Bresch, J. Lemoine, F. Guillen-Gonzalez. A note on a de- generate elliptic equation with applications for seas and lakes, Elect. J. Diff. Eqs, 42, 1–13, (2004).

[24] D. Bresch, J. Koko. An optimization–based domain decomposition method for nonlinearly wall laws in coupled systems, Math. Models. Methods Appl. Sci., vol. 14, 7, 1085–1101, (2004).

[25] D. Bresch, B. Desjardins. Quelques mod`eles diffusifs capillaires de type Korteweg, C. R. Acad. Sci. Paris, section m ́ecanique, 332, no. 11, 881–886, (2004).

[26] D. Bresch, A. Kazhikhov, J. Lemoine. On the two-dimensional hydrostatic Navier-Stokes equations, SIAM J. Math. Anal., 36, 3, 796–814, (2004).

[27] D. Bresch, B. Desjardins, B. Ducomet. Quasi-neutral limit for a viscous capillary model of plasma, Annales I.H.P., 22, 1, 1–9, (2005).

[28] D. Bresch, D. Gérard-Varet. About roughness-induced effects on the quasi-geostrophic model, Commun. Math. Phys., 253, 1, 81–119, (2005).

[29] D. Bresch, M. Gisclon, C.K. Lin An example of Low mach (Froude) number effects for compressible flows with nonconstant density (height) limit, M2AN, 39, 3, 477–486, (2005).

[30] D. Bresch, G. Métivier. Global existence and uniqueness for the lake equations with vanishing topography: elliptic estimates for degenerate equations, Nonlinearity, 19, no. 3, 591–610 (2006).

[31] D. Bresch, D. Gérard-Varet, E. Grenier. On the derivation of the planetary geostrophic equations, Arch. Rat. Mech. Anal., 182, 3, 387–413 (2006).

[32] D. Bresch, D. Gérard-Varet. On some homogeneization problems from shallow water theory. Applied Math. Letters, 20, Issue 5, 505–510, (2006).

[33] D. Bresch, B. Desjardins. On the construction of approximate solutions for the 2D viscous shallow water model and for compressible Navier- Stokes models. J. Maths. Pures et Appliqu ́ees, 86, 4, 362–368 (2006).

[34] B. Ribba, O. Saut, T. Colin, D. Bresch, E. Grenier, J.P. Boissel. A multiscale mathematical model of avascular tumor growth to investi- gate the therapeutic benefit of anti-invasive agents. J. Theoret. Biol. 243 (2006), no. 4, 532–541.

[35] D. Bresch, B. Desjardins. On the existence of global weak solutions to the Navier-Stokes equations for viscous compressible and heat conducting fluids. J. Math. Pures Appl. (9) 87 (2007), no. 1, 57–90. Extension de : D. Bresch, B. Desjardins. Stabilité de solutions faibles pour les équations de Navier-Stokes compressibles avec conductivité de chaleur. C.R. Acad. Sciences Paris, Section Mathématiques, vol. 343, Issue 3, 219– 224, (2006).

[36] D. Bresch, B. Desjardins, D. Gérard-Varet. On compressible Navier-Stokes equations with density dependent viscosities in bounded domains. J. Math. Pures Appl. (9) 87 (2007), no. 2, 227–235.

[37] D. Bresch, E.H. Essoufi, M. Sy. Effect of density dependent viscosities on multiphasic incompressible fluid models. J. Math. Fluid Mech. 9 (2007), no. 3, 377–397. Extension de : D. Bresch, E.H. Essoufi, M. Sy. De nouveaux systèmes de type Kazhikhov-Smagulov : modèles de propagation de polluants et de combustion à faible nombre de Mach, C. R. Acad. Sci. Paris, 335, Série I, (2002), 973–978.

[38] D. Bresch, B. Desjardins, E. Grenier. Crossing of eigenvalues: measure type estimates. J. Differential Equations 241 (2007), no. 2, 207–224.

[39] D. Bresch, P. Noble. Mathematical Justification of a Shallow Water Model. Methods and Applications of Analysis, 87–118, (2007).

[40] D. Bresch, B. Desjardins, M. Gisclon, R. Sart. Some instability results on the compressible Korteweg model, Ann. Univ. Ferrara, Volume 54, Number 1, 11–36,(2008).

[41] D. Bresch, B. Desjardins, E. Grenier. Measures on double or resonant eigenvalues for linear Schrodinger operator. J. Funct. Anal. 254, No5, 1269–1281, (2008).

[42] E. Fernandez-Nieto, D. Bresch, J. Monnier. Well-balanced HLLC solvers for non-homogeneous shallow-water equations with consistent intermediate wave speed. C. R. Math., 346 (13–14), 795–800, (2008).

[43] E.D. Fernandez-Nieto, F. Bouchut, D. Bresch, M.J. Castro- Diaz, A. Mangeney. A new Savage–Hutter type model for submarine avalanches and generated tsunami. J. Comp. Phys., 227, 16, 7720–7754, (2008).

[44] F. Billy, O. Saut, H. Morre-Trouilhet, T. Colin, D. Bresch, B. Ribba, E. Grenier, J.P. Flandrois. Modèle mathématique multi-échelle de l’angiogense tumorale et application à l’analyse de l’efficacité de traitements anti-angiogéniques. Bull Cancer 95(NS): 65, (2008).

[45] D. Bresch, B. Desjardins, J.–M. Ghidaglia, E. Grenier. On global weak solutions to a generic two-fluid model. Arch. Rational Mech. Anal. Volume 196, Number 2, 599-629, (2009).

[46] B. Bouffandeau, D. Bresch, B. Desjardins, E. Grenier. Exis- tence of compactly supported solutions for a degenerate nonlinear parabolic equation with nonlipschitz source term. Methods Appl. Anal. volume 16, Number 1 (2009), 45–54.

[47] D. Bresch, T. Colin, E. Grenier, B. Ribba, O. Saut. A vis- coelastic model for avascular tumor growth. DCDS, 101 – 108, (2009).

[48] F. Billy, B. Ribba, O. Saut, H. Morre-Trouilhet, T. Colin, D. Bresch, JP. Boissel, E. Grenier, JP. Flandrois. A pharmacologically based multiscale mathematical model of angiogenesis and its use in investigating the efficacy of a new cancer treatment strategy. J Theor Biol,260(4), (2009), 545–562.

[49] E. Grenier, D. Bresch, M.–A. Dronne, M. Hommel, J.–P. Boissel. A phenomenological model of the growth of the necrotic area in ischemie stroke, Math. & Computer Modeling (2010), vol. 51, no9-10, 1011–1025.

[50] D. Bresch, V. Milisic. High order multi-scale wall laws, part I : the periodic case. Quarterly Applied Math., Vol. LXVIII, No. 2. (June 2010), pp. 229-253. Extension de : D. Bresch, V. Milisic. Vers des lois de parois multi-échelles implicites. Towards implicit multi-scale wall laws. C. R. Math. Acad. Sci. Paris 346 (2008), no. 15–16.

[51] D. Bresch, T. Colin, E. Grenier, B. Ribba, O. Saut. Computational Modeling of avascular tumor growth: the avascular stage. SIAM Journal of Scientific Computing 32 (4), 2321–2344, (2010).

[52] D. Bresch, C. Choquet, L. Chupin, Th. Colin, M. Gisclon. Roughness-induced effect at main order on the Reynolds approximation. SIAM Multiscale Model. Simul., (2010), vol. 8(3), 997–1017. Un erratum est disponible sur https://pageperso.univ-lr.fr/cchoquet/err_SIAM-MMS.pdf

[53] D. Bresch, G. Métivier. Anelastic limits for euler type systems. Appl. Math Res Express, 2, 119–141, (2010).

[54] R. Klein, U. Achatz, D. Bresch, O.M. Knio, P.K. Smola- rkiewicz. Regime of validity of sound-proof atmosphere flow models. J. Atmos. Sci., 67, 3226–3237, (2010).

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