Open Access
Volume 57, Number 6, November-December 2023
Page(s) 3403 - 3437
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]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you