Geodesic
Stochastic scalar conservation laws driven by rough paths
Annales de l'I.H.P. Analyse non linéaire, Tome 33 (2016) no. 4, pp. 933-963

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We prove the existence and uniqueness of solutions to a class of stochastic scalar conservation laws with joint space–time transport noise and affine-linear noise driven by a geometric p-rough path. In particular, stability of the solutions with respect to the driving rough path is obtained, leading to a robust approach to stochastic scalar conservation laws. As immediate corollaries we obtain support theorems, large deviation results and the generation of a random dynamical system.

DOI : 10.1016/j.anihpc.2015.01.009
Classification : H6015, 35R60, 35L65
Keywords: Stochastic scalar conservation laws, Rough paths, Random dynamical systems, Stability, Kružkov entropy solutions 
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     title = {Stochastic scalar conservation laws driven by rough paths},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {933--963},
     publisher = {Elsevier},
     volume = {33},
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     year = {2016},
     doi = {10.1016/j.anihpc.2015.01.009},
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     zbl = {1345.60055},
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     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2015.01.009/}
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Friz, Peter K.; Gess, Benjamin. Stochastic scalar conservation laws driven by rough paths. Annales de l'I.H.P. Analyse non linéaire, Tome 33 (2016) no. 4, pp. 933-963. doi: 10.1016/j.anihpc.2015.01.009

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