Open Access
Issue
ESAIM: M2AN
Volume 57, Number 6, November-December 2023
Page(s) 3403 - 3437
DOI https://doi.org/10.1051/m2an/2023085
Published online 29 November 2023
  1. E.J. Balder, Lectures on Young measure theory and its applications in economics. Rend. Iftit. Mat. Univ. Trieste 31 (2001) 1–69. [Google Scholar]
  2. P. Baldi, Stochastic Calculus: An Introduction Through Theory and Exercises, Universitext Springer, Cham (2017) xiv + 627 pp. [Google Scholar]
  3. F. Berthelin and J. Vovelle, Stochastic isentropic Euler equations. Ann. Sci. Ec. Norm. Super 52 (2019) 181–254. [CrossRef] [MathSciNet] [Google Scholar]
  4. N. Bhauryal, U. Koley and G. Vallet, The Cauchy problem for a fractional conservation laws driven by Lévy noise. Stoch. Processes App. 130 (2020) 5310–5365. [CrossRef] [Google Scholar]
  5. N. Bhauryal, U. Koley and G. Vallet, A fractional degenerate parabolic-hyperbolic Cauchy problem with noise. J. Diff. Equ. 284 (2021) 433–521. [CrossRef] [Google Scholar]
  6. I.H. Biswas, U. Koley and A.K. Majee, Continuous dependence estimate for conservation laws with Lévy noise. J. Diff. Equ. 259 (2015) 4683–4706. [CrossRef] [Google Scholar]
  7. D. Breit and P.R. Mensah, Stochastic compressible Euler equations and inviscid limits. Nonlinear Anal. 184 (2019) 218–238. [CrossRef] [MathSciNet] [Google Scholar]
  8. D. Breit and T.C. Moyo, Dissipative solutions to the stochastic Euler equations. J. Math. Fluid Mech. 23 (2021) 23. [CrossRef] [Google Scholar]
  9. D. Breit, E. Feireisl and M. Hofmanová, Stochastically Forced Compressible Fluid Flows. De Gruyter Series in Applied and Numerical Mathematics, De Gruyter, Berlin/Munich/Boston (2018). [Google Scholar]
  10. D. Breit, E. Feireisl and M. Hofmanová, On solvability and ill-posedness of the compressible Euler system subject to stochastic forces. Anal. PDE 13 (2020) 371–402. [CrossRef] [MathSciNet] [Google Scholar]
  11. D. Breit, E. Feireisl and M. Hofmanová, Solution semiflow for the isentropic Euler system. Arch. Ration. Mech. Anal. 235 (2020) 167–194. [CrossRef] [MathSciNet] [Google Scholar]
  12. Z. Brzeźniak, B. Maslowski and J. Seidler, Stochastic nonlinear beam equations. Probab. Theory Related Fields 132 (2005) 119–149. [CrossRef] [MathSciNet] [Google Scholar]
  13. T. Buckmaster, S. Shkoller and V. Vicol, Formation of shocks for 2D isentropic compressible Euler. Commun. Pure. Appl. Math. 75 (2022) 2069–2120. [Google Scholar]
  14. T. Buckmaster, S. Shkoller and V. Vicol, Formation of point shocks for 3D compressible Euler. Commun. Pure Appl. Math. 76 (2023) 2073–2191. [CrossRef] [Google Scholar]
  15. A. Chaudhary and U. Koley, On weak-strong uniqueness for stochastic equations of incompressible fluid flow. J. Math. Fluid Mech. 24 (2022) 33. [CrossRef] [Google Scholar]
  16. E. Chiodaroli, O. Kreml, V. Mácha and S. Schwarzacher, Non-uniqueness of admissible weak solutions to the compressible Euler equations with smooth initial data. Trans. Am. Math. Soc. 374 (2021) 2269–2295. [CrossRef] [Google Scholar]
  17. C. De Lellis and L. Székelyhidi, Jr., On admissibility criteria for weak solutions of the Euler equations. Arch. Ration. Mech. Anal. 195 (2010) 225–260. [CrossRef] [MathSciNet] [Google Scholar]
  18. C. De Lellis and L. Székelyhidi Jr, The h-principle and the equations of fluid dynamics. Bull. Amer. Math. Soc. (N.S.) 49 (2012) 347–375. [CrossRef] [MathSciNet] [Google Scholar]
  19. V. Elling, A possible counterexample to well posedness of entropy solutions and Godunov scheme convergence. Math. Comput. 75 (2006) 1721–1733. [CrossRef] [Google Scholar]
  20. K.D. Elworthy, Stochastic Differential Equations on Manifolds. Vol. 70 of London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge-New York (1982). [Google Scholar]
  21. E. Feireisl, Weak solutions to problems involving inviscid fluids, in Mathematical Fluid Dynamics, Present and Future. Springer Proceedings in Mathematics and Statistics. Vol. 183. Springer, New York (2016) 377–399. [CrossRef] [Google Scholar]
  22. E. Feireisl, M. Lukáčová-Medvid’ová, Convergence of a mixed finite element finite volume scheme for the isentropic Navier-Stokes system via dissipative measure-valued solutions. Found. Comput. Math. 18 (2018) 703–730. [CrossRef] [MathSciNet] [Google Scholar]
  23. E. Feireisl, P. Gwiazda, A. Świerczewska-Gwiazda and E. Wiedemann, Dissipative measure-valued solutions to the compressible Navier-Stokes system. Calc. Var. Part. Differ. Equ. 55 (2016) 141. [CrossRef] [Google Scholar]
  24. E. Feireisl and M. Lukáčová-Medvid’ová and H. Mizerová, Convergence of finite volume schemes for the Euler equations via dissipative measure-valued solutions. Found. Comput. Math. 20 (2020) 923–966. [CrossRef] [MathSciNet] [Google Scholar]
  25. E. Feireisl, M. Lukáčová-Medvid’ová and H. Mizerová, K-convergence as a new tool in numerical analysis. IMA J. Numer. Anal. 40 (2020) 2227–2255. [CrossRef] [MathSciNet] [Google Scholar]
  26. U.S. Fjordholm, S. Mishra and E. Tadmor, On the computation of measure-valued solutions. Acta Numer. 25 (2016) 567–679. [Google Scholar]
  27. U.S. Fjordholm, R. Käppeli, S. Mishra and E. Tadmor, Construction of approximate entropy measure valued solutions for hyperbolic systems of conservation laws. Found. Comp. Math. 17 (2017) 763–827. [CrossRef] [Google Scholar]
  28. F. Flandoli and D. Gatarek, Martingale and stationary solutions for stochastic Navier-Stokes equations. Probab. Theory Relat. Fields 102 (1995) 367–391. [Google Scholar]
  29. P. Gwiazda, A. Swierczewska-Gwiazda and E. Wiedemann, Weak–strong uniqueness for measure-valued solutions of some compressible fluid models. Nonlinearity 28 (2015) 3873–3890. [CrossRef] [MathSciNet] [Google Scholar]
  30. M. Hofmanova, U. Koley and U. Sarkar, Measure-valued solutions to the stochastic compressible Euler equations and incompressible limits. Comm. Part. Differ. Equ. 47 (2022) 1907–1943. [CrossRef] [Google Scholar]
  31. A. Jakubowski, The almost sure Skorokhod representation for subsequences in nonmetric spaces. Theory Probab. Appl. 42 (1998) 164–174. [Google Scholar]
  32. T. Karper, A convergent FEM-DG method for the compressible Navier-Stokes equations. Numer. Math. 125 (2013) 441–510. [Google Scholar]
  33. U. Koley and G. Vallet, On the rate of convergence of a numerical scheme for fractional conservation laws with noise. IMA J. Numer. Anal. to appear (2023). DOI: 10.1093/imanum/drad015. [Google Scholar]
  34. U. Koley, A.K. Majee and G. Vallet, Continuous dependence estimate for a degenerate parabolic-hyperbolic equation with Lévy noise. Stoch. Part. Differ. Equ. Anal. Comput. 5 (2017) 145–191. [Google Scholar]
  35. U. Koley, N.H. Risebro, C. Schwab and F. Weber, A multilevel Monte Carlo finite difference method for random scalar degenerate convection-diffusion equations. J. Hyperbolic Differ. Equ. 14 (2017) 415–454. [CrossRef] [MathSciNet] [Google Scholar]
  36. U. Koley, A.K. Majee and G. Vallet, A finite difference scheme for conservation laws driven by Lévy noise. IMA J. Numer. Anal. 38 (2018) 998–1050. [CrossRef] [MathSciNet] [Google Scholar]
  37. U. Koley, D. Ray and T. Sarkar, Multi-level Monte Carlo finite difference methods for fractional conservation laws with random data. SIAM/ASA J. Uncertain. Quantif. 9 (2021) 65–105. [CrossRef] [MathSciNet] [Google Scholar]
  38. J. Málek, J. Necas, M. Rokyta and M. Ruzicka, Weak and Measure-Valued Solutions to Evolutionary PDEs. Vol. 13, CRC Press, Boca Raton (1996). [CrossRef] [Google Scholar]
  39. E. Motyl, Stochastic Navier-Stokes equations driven by Lévy noise in unbounded 3D domains. Potential Anal. 38 (2012) 863–912. [Google Scholar]
  40. J. Neustupa, Measure-valued solutions of the Euler and Navier-Stokes equations for compressible barotropic fluids. Math. Nachr. 163 (1993) 217–227. [CrossRef] [MathSciNet] [Google Scholar]
  41. M. Ondreját, Stochastic nonlinear wave equations in local Sobolev spaces. Electron. J. Probab. 15 (2010) 1041–1091. [MathSciNet] [Google Scholar]
  42. E. Tadmor, Entropy stability theory for difference approximations of nonlinear conservation laws and related time dependent problems. Acta Numer. 12 (2003) 451–512. [CrossRef] [MathSciNet] [Google Scholar]
  43. G. Vallet and A. Zimmermann, Well-posedness for nonlinear SPDEs with strongly continuous perturbation. Proc. R. Soc. Edinburgh: Sect. A Math., 151 (2021) 265–295. [CrossRef] [Google Scholar]

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