S. E. Audusse, N. Boyaval, M. Goutal, P. Jodeau, and . Ung, Numerical simulation of the dynamics of sedimentary river beds with a stochastic Exner equation, ESAIM: Proceedings and Surveys, vol.48, issue.48, pp.321-340, 2015.
DOI : 10.1051/proc/201448015

URL : https://hal.archives-ouvertes.fr/hal-01102335

G. [. Attouch, G. Buttazzo, and . Michaille, Variational analysis in Sobolev and BV spaces, MPS/SIAM Series on Optimization Society for Industrial and Applied Mathematics (SIAM), vol.6, 2006.
DOI : 10.1137/1.9781611973488

]. H. Bes99 and . Bessaih, Martingale solutions for stochastic Euler equations, Stochastic Anal, Appl, vol.17, issue.5, pp.713-725, 1999.

F. [. Bessaih and . Flandoli, 2-D Euler equation perturbed by noise, NoDEA : Nonlinear Differential Equations and Applications, vol.6, issue.1, pp.35-54, 1999.
DOI : 10.1007/s000300050063

E. [. Breit, M. Feireisl, and . Hofmanová, Incompressible Limit for Compressible Fluids with Stochastic Forcing, Archive for Rational Mechanics and Analysis, vol.7, issue.4, 2015.
DOI : 10.1007/s00205-016-1014-y

F. [. Brze´zniakbrze´zniak, M. Flandoli, and . Maurelli, Existence and uniqueness for stochastic 2d euler flows with bounded vorticity, 2014.

M. [. Breit and . Hofmanová, Stochastic navier-stokes equations for compressible fluids, 2014.

]. P. Bil99 and . Billingsley, Convergence of probability measures, second ed., Wiley Series in Probability and Statistics: Probability and Statistics, 1999.

M. [. Brze´zniakbrze´zniak and . Ondreját, Weak Solutions to Stochastic Wave Equations with Values in Riemannian Manifolds, Communications in Partial Differential Equations, vol.232, issue.9, pp.1624-1653, 2011.
DOI : 10.1090/S0273-0979-04-01005-5

S. [. Brze´zniakbrze´zniak and . Peszat, Stochastic two dimensional Euler equations, Ann. Probab, vol.29, issue.4, pp.1796-1832, 2001.

R. [. Brze´zniakbrze´zniak and . Serrano, Optimal Relaxed Control of Dissipative Stochastic Partial Differential Equations in Banach Spaces, SIAM Journal on Control and Optimization, vol.51, issue.3, pp.2664-2703, 2013.
DOI : 10.1137/100788574

C. Bauzet, G. Vallet, and P. Wittbold, THE CAUCHY PROBLEM FOR CONSERVATION LAWS WITH A MULTIPLICATIVE STOCHASTIC PERTURBATION, Journal of Hyperbolic Differential Equations, vol.09, issue.04, pp.661-709, 2012.
DOI : 10.1142/S0219891612500221

URL : https://hal.archives-ouvertes.fr/hal-01309552

M. Capi´nskicapi´nski and N. J. Cutland, Stochastic Euler equations on the torus, Ann. Appl. Probab, vol.9, issue.3, pp.688-705, 1999.

C. [. Chueh, J. A. Conley, and . Smoller, Positively invariant regions for systems of nonlinear diffusion equations, Math. J, vol.26, issue.2, pp.373-392, 1977.

[. Chen, Q. Ding, and K. H. Karlsen, On Nonlinear Stochastic Balance Laws, Archive for Rational Mechanics and Analysis, vol.12, issue.4, pp.707-743, 2012.
DOI : 10.1007/s00205-011-0489-9

[. Chen and H. Frid, Decay of Entropy Solutions of Nonlinear Conservation Laws, Archive for Rational Mechanics and Analysis, vol.146, issue.2, pp.95-127, 1999.
DOI : 10.1007/s002050050138

[. Cruzeiro, F. Flandoli, and P. Malliavin, Brownian motion on volume preserving diffeomorphisms group and existence of global solutions of 2D stochastic Euler equation, Journal of Functional Analysis, vol.242, issue.1, pp.304-326, 2007.
DOI : 10.1016/j.jfa.2006.06.010

A. [. Cazenave and . Haraux, An introduction to semilinear evolution equations, Oxford Lecture Series in Mathematics and its Applications, 1998.

G. Q. Chen, Convergence of the Lax-Friedrichs scheme for isentropic gas dynamics, III, Acta Math. Sci. (English Ed.), vol.6, issue.1, pp.75-120, 1986.

]. C. Crdfv04, P. Castaing, M. Raynaud-de-fitte, and . Valadier, Young measures on topological spaces, Mathematics and its Applications, 2004.

[. Cruzeiro and I. Torrecilla, On a 2D stochastic Euler equation of transport type: existence and geometric formulation Uniqueness of renormalized solutions of degenerate elliptic-parabolic problems, Stoch. Dyn. J. Differential Equations, vol.15, issue.156 1, pp.93-121, 1999.

G. [. Ding, P. Z. Chen, and . Luo, Convergence of the Lax-Friedrichs scheme for isentropic gas dynamics. I, II, Acta Math. Sci. (English Ed.), vol.5, issue.4, pp.415-432, 1985.

. [. Doleans-dade, Stochastic processes and stochastic differential equations, Stochastic differential equations, C.I.M.E. Summer Sch, vol.77, pp.5-73, 2010.

M. [. Debussche, J. Hofmanová, and . Vovelle, Degenerate parabolic stochastic partial differential equations: Quasilinear case, The Annals of Probability, vol.44, issue.3, 2015.
DOI : 10.1214/15-AOP1013

URL : https://hal.archives-ouvertes.fr/hal-00863829

]. R. Dip83a and . Diperna, Convergence of approximate solutions to conservation laws, Arch. Rational Mech. Anal, vol.82, issue.1, pp.27-70, 1983.

]. R. Dip83b and . Diperna, Convergence of the viscosity method for isentropic gas dynamics, Comm. Math. Phys, issue.1, pp.91-92, 1983.

J. [. Debussche and . Vovelle, Scalar conservation laws with stochastic forcing, Journal of Functional Analysis, vol.259, issue.4, pp.1014-1042, 2010.
DOI : 10.1016/j.jfa.2010.02.016

URL : https://hal.archives-ouvertes.fr/hal-00451641

E. Weinan, K. Khanin, A. Mazel, and Y. Sinai, Invariant measures for Burgers equation with stochastic forcing, Ann. of Math, vol.151, issue.2 3, pp.877-960, 2000.
DOI : 10.1007/978-1-4419-6205-8_17

B. [. Feireisl, A. Maslowski, and . Novotn´ynovotn´y, Compressible fluid flows driven by stochastic forcing, Journal of Differential Equations, vol.254, issue.3, pp.1342-1358, 2013.
DOI : 10.1016/j.jde.2012.10.020

URL : https://hal.archives-ouvertes.fr/hal-01284103

D. [. Feng and . Nualart, Stochastic scalar conservation laws, Journal of Functional Analysis, vol.255, issue.2, pp.313-373, 2008.
DOI : 10.1016/j.jfa.2008.02.004

V. [. Glatt-holtz and . Vicol, Local and global existence of smooth solutions for the stochastic Euler equations with multiplicative noise, The Annals of Probability, vol.42, issue.1, pp.80-145, 2014.
DOI : 10.1214/12-AOP773

I. Gyöngy and N. Krylov, Existence of strong solutions for Itô's stochastic equations via approximations, Probab. Theory Related Fields, pp.143-158, 1996.

P. [. Glimm and . Lax, Decay of solutions of systems of nonlinear hyperbolic conservation laws, Memoirs of the, 1970.

[. Gerbeau and B. Perthame, Derivation of viscous Saint-Venant system for laminar shallow water; numerical validation, Discrete Contin, Dyn. Syst. Ser. B, vol.1, issue.1, pp.89-102, 2001.

. [. Gess and P. E. Souganidis, Long-Time Behavior, Invariant Measures, and Regularizing Effects for Stochastic Scalar Conservation Laws, Communications on Pure and Applied Mathematics, vol.12, issue.4, pp.1411-3939, 2014.
DOI : 10.1142/S0219025709003872

I. Gyöngy and C. Rovira, On L p -solutions of semilinear stochastic partial differential equations, Stochastic Process, Appl, vol.90, issue.1, pp.83-108, 2000.

]. M. Hof13 and . Hofmanová, Degenerate parabolic stochastic partial differential equations, Stochastic Process, Appl, vol.123, issue.12, pp.4294-4336, 2013.

J. [. Hofmanová and . Seidler, On Weak Solutions of Stochastic Differential Equations, Stochastic Analysis and Applications, vol.2, issue.1, pp.100-121, 2012.
DOI : 10.1080/07362994.2012.628916

]. Y. Kim03 and . Kim, Asymptotic behavior of solutions to scalar conservation laws and optimal convergence orders to N-waves, Journal of Differential Equations, vol.192, issue.1, pp.202-224, 2003.
DOI : 10.1016/S0022-0396(03)00058-5

]. J. Kim11 and . Kim, On the stochastic quasi-linear symmetric hyperbolic system, Journal of Differential Equations, vol.250, issue.3, pp.1650-1684, 2011.
DOI : 10.1016/j.jde.2010.09.025

[. Lions, B. Perthame, and P. E. Souganidis, Existence and stability of entropy solutions for the hyperbolic systems of isentropic gas dynamics in Eulerian and Lagrangian coordinates, Communications on Pure and Applied Mathematics, vol.4, issue.6, pp.599-638, 1996.
DOI : 10.1002/(SICI)1097-0312(199606)49:6<599::AID-CPA2>3.0.CO;2-5

]. Lps13a, B. Lions, P. E. Perthame, and . Souganidis, Scalar conservation laws with rough (stochastic) fluxes, Stoch. Partial Differ, Equ. Anal. Comput, vol.1, issue.4, pp.664-686, 2013.

[. Lions, B. Perthame, and E. Tadmor, Kinetic formulation of the isentropic gas dynamics andp-systems, Communications in Mathematical Physics, vol.13, issue.3???4, pp.415-431, 1994.
DOI : 10.1007/BF02102014

O. A. Lady?enskaja, V. A. Solonnikov, and N. N. , Ural ceva, Linear and quasilinear equations of parabolic type, Translated from the Russian by S, Smith. Translations of Mathematical Monographs, vol.23, 1968.

M. [. Lefloch and . Westdickenberg, Finite energy solutions to the isentropic Euler equations with geometric effects, Journal de Math??matiques Pures et Appliqu??es, vol.88, issue.5, pp.389-429, 2007.
DOI : 10.1016/j.matpur.2007.07.004

]. F. Mur78 and . Murat, Compacité par compensation, Ann. Scuola Norm, Sup. Pisa Cl. Sci, vol.4, issue.5 3, pp.489-507, 1978.

A. [. Mellet and . Vasseur, A bound from below for the temperature in compressible Navier???Stokes equations, Monatshefte f??r Mathematik, vol.14, issue.5???6, pp.143-161, 2009.
DOI : 10.1007/s00605-008-0021-y

]. L. Nir59 and . Nirenberg, On elliptic partial differential equations, Ann. Scuola Norm. Sup. Pisa, vol.13, issue.3, pp.115-162, 1959.

]. M. Ond10 and . Ondreját, Stochastic nonlinear wave equations in local Sobolev spaces, Electron, J. Probab, vol.15, issue.33, pp.1041-1091, 2010.

]. D. Ser96 and . Serre, Systèmes de lois de conservation. II, Diderot Editeur Structures géométriques, oscillation etprobì emes mixtes. [Geometric structures, oscillation and mixed problems, 1996.

]. J. Sim87 and . Simon, Compact sets in the space L p (0, Ann. Mat. Pura Appl, vol.146, issue.4, pp.65-96, 1987.

]. A. Sko56 and . Skorohod, Limit theorems for stochastic processes, Teor. Veroyatnost. i Primenen, vol.1, pp.289-319, 1956.

]. S. Smi15 and . Smith, Random perturbations of viscous compressible fluids: Global existence of weak solutions, 2015.

G. Stampacchia, Le probl??me de Dirichlet pour les ??quations elliptiques du second ordre ?? coefficients discontinus, Annales de l???institut Fourier, vol.15, issue.1, pp.189-258, 1965.
DOI : 10.5802/aif.204

H. [. Tornatore and Y. Fujita, One-dimensional stochastic equations for a viscous barotropic gas, Ricerche Mat, vol.46, issue.2, pp.255-283, 1997.

]. H. Tri92 and . Triebel, Theory of function spaces, II, Monographs in Mathematics, vol.84, 1992.

P. [. Vallet and . Wittbold, ON A STOCHASTIC FIRST-ORDER HYPERBOLIC EQUATION IN A BOUNDED DOMAIN, Infinite Dimensional Analysis, Quantum Probability and Related Topics, vol.12, issue.04, pp.613-651, 2009.
DOI : 10.1142/S0219025709003872

URL : https://hal.archives-ouvertes.fr/hal-00866266