Books, Proceedings and Seminars of Centre Mersenne

[1] Alazard, T., Burq, N., and Zuily C., On the Cauchy problem for gravity water waves, preprint 2012, . | arXiv | MR

[2] Alazard, T., Burq, N., and Zuily C., On the Water Waves Equations with Surface Tension, Duke Math. J. 158 3 (2011), 413-499. | MR | Zbl

[3] Alinhac, S., Existence d’ondes de raréfaction pour des systèmes quasi-linéaires hyperboliques multidimensionnels. Comm. Partial Differential Equations 14, 2(1989), 173–230. | MR | Zbl

[4] Bardos, C., Existence et unicité de la solution de l’équation d’Euler en dimension deux. J. Math. Anal. Appl. 40 (1972), 769–790. | MR | Zbl

[5] Bardos, C. and Rauch, J., Maximal positive boundary value problems as limits of singular perturbation problems. Trans. Amer. Math. Soc. 270, 2 (1982), 377–408. | MR | Zbl

[6] Beale, J. T., The initial value problem for the Navier-Stokes equations with a free surface. Comm. Pure Appl. Math. 34, 3 (1981), 359–392. | MR | Zbl

[7] Beirão da Veiga, H., Vorticity and regularity for flows under the Navier boundary condition. Commun. Pure Appl. Anal. 5, 4 (2006), 907–918. | MR | Zbl

[8] Beirão da Veiga, H. and Crispo, F., Concerning the $W^{k,p}$-inviscid limit for 3-d flows under a slip boundary condition. J. Math. Fluid Mech. | MR

[9] Bony, J.-M., Calcul symbolique et propagation des singularités pour les équations aux dŽrivées partielles non linéaires. Ann. Sci. Ecole Norm. Sup. (4) 14, 2(1981). | EuDML | Numdam | MR | Zbl

[10] Christodoulou, D. and Lindblad, H., On the motion of the free surface of a liquid. Comm. Pure Appl. Math. 53, 12(2000), 1536–1602. | MR | Zbl

[11] Clopeau, T., Mikelić, A., and Robert, R., On the vanishing viscosity limit for the $2\mathrm{D}$ incompressible Navier-Stokes equations with the friction type boundary conditions. Nonlinearity 11, 6 (1998), 1625–1636. | MR | Zbl

[12] Coutand, D. and Shkoller S., Well-posedness of the free-surface incompressible Euler equations with or without surface tension, J. Amer. Math. Soc., 20 (2007),829–930. | MR | Zbl

[13] GŽrard-Varet, D. and Dormy, E., On the ill-posedness of the Prandtl equation. J. Amer. Math. Soc. 23, 2(2010), 591–609 | MR | Zbl

[14] Germain, P., Masmoudi, N., and Shatah, J., Global solutions for the gravity water waves in dimension 3, . | arXiv

[15] Gisclon, M. and Serre, D., Étude des conditions aux limites pour un système strictement hyperbolique via l’approximation parabolique. C. R. Acad. Sci. Paris Sér. I Math. 319, 4 (1994), 377–382. | MR | Zbl

[16] Grenier, E., On the nonlinear instability of Euler and Prandtl equations. Comm. Pure Appl. Math. 53, 9(2000),1067–1091. | MR | Zbl

[17] Grenier, E. and Guès, O., Boundary layers for viscous perturbations of noncharacteristic quasilinear hyperbolic problems. J. Differential Equations 143, 1 (1998), 110–146. | MR | Zbl

[18] Grenier, E. and Rousset, F., Stability of one-dimensional boundary layers by using Green’s functions. Comm. Pure Appl. Math. 54, 11 (2001), 1343–1385. | MR | Zbl

[19] Guès, O., Problème mixte hyperbolique quasi-linéaire caractéristique. Comm. Partial Differential Equations 15, 5 (1990), 595–645. | MR | Zbl

[20] Guès, O., Métivier, G., Williams, M., and Zumbrun, K., Existence and stability of noncharacteristic boundary layers for the compressible Navier-Stokes and viscous MHD equations. Arch. Ration. Mech. Anal. 197, 1(2010), 1–87. | MR | Zbl

[21] Guo, Y. and Nguyen T., A note on the Prandtl boundary layers, . | arXiv | MR

[22] Hörmander, L., Pseudo-differential operators and non-elliptic boundary problems. Ann. of Math. (2) 83 (1966), 129–209. | MR | Zbl

[23] Iftimie, D. and Planas, G., Inviscid limits for the Navier-Stokes equations with Navier friction boundary conditions. Nonlinearity 19, 4 (2006), 899–918. | MR | Zbl

[24] Iftimie, D. and Sueur, F., Viscous boundary layers for the Navier-Stokes equations with the Navier slip conditions. Arch. Rat. Mech. Analysis, available online. | Zbl

[25] Kelliher, J. P., Navier-Stokes equations with Navier boundary conditions for a bounded domain in the plane. SIAM J. Math. Anal. 38, 1 (2006), 210–232 (electronic). | MR

[26] Lannes, D., Well-posedness of the water-waves equations, Journal AMS 18 (2005) 605-654. | MR | Zbl

[27] Lindblad, H., Well-posedness for the linearized motion of an incompressible liquid with free surface boundary. Comm. Pure Appl. Math. 56. 2(2003), 153–197. | MR | Zbl

[28] Lindblad, H., Well-posedness for the motion of an incompressible liquid with free surface boundary. Ann. of Math. (2) 162. 1 (2005), 109–194. | MR | Zbl

[29] Masmoudi, N. and Rousset F., Uniform regularity for the Navier-Stokes equation with Navier boundary condition, Arch. Ration. Mech. Anal. 203 (2012), no. 2, 529Ð575. | MR

[30] Masmoudi, N. and Rousset F., Vanishing viscosity limit for the free surface compressible Navier-Stokes system, in preparation.

[31] Masmoudi, N. and Rousset F., Uniform regularity and vanishing viscosity limit for the free surface Navier-Stokes equation, preprint 2012, . | arXiv | MR

[32] Métivier, G. and Zumbrun K., Large viscous boundary layers for noncharacteristic nonlinear hyperbolic problems. Mem. Amer. Math. Soc. 175 2005, 826. | MR | Zbl

[33] Rousset, F., Characteristic boundary layers in real vanishing viscosity limits. J. Differential Equations 210, 1 (2005), 25–64. | MR | Zbl

[34] Sammartino, M. and Caflisch, R. E., Zero viscosity limit for analytic solutions, of the Navier-Stokes equation on a half-space. I. Existence for Euler and Prandtl equations. Comm. Math. Phys. 192, 2 (1998), 433–461. | MR | Zbl

[35] Shatah, J. and Zeng, C., Geometry and a priori estimates for free boundary problems of the Euler equation, Comm. Pure Appl. Math., 61 (2008), 698–744. | MR | Zbl

[36] Tani, A. and Tanaka, N., Large-time existence of surface waves in incompressible viscous fluids with or without surface tension. Arch. Rational Mech. Anal. 130, 4(1995), 303–314. | MR | Zbl

[37] Tartakoff, D. S., Regularity of solutions to boundary value problems for first order systems. Indiana Univ. Math. J. 21 (1971/72), 1113–1129. | MR | Zbl

[38] Temam, R. and Wang, X., Boundary layers associated with incompressible Navier-Stokes equations: the noncharacteristic boundary case. J. Differential Equations 179, 2 (2002), 647–686. | MR | Zbl

[39] Xiao, Y. and Xin, Z., On the vanishing viscosity limit for the 3D Navier-Stokes equations with a slip boundary condition. Comm. Pure Appl. Math. 60, 7 (2007), 1027–1055. | MR | Zbl

[40] Wu, S., Well-posedness in Sobolev spaces of the full water wave problem in 3-D, J. Amer. Math. Soc.,12 (1999), 445–495. | MR | Zbl

[41] Wu, S., Global wellposedness of the 3-D full water wave problem. Invent. Math. 184, 1(2011), 125–220. | MR | Zbl