Invariant measure of scalar first-order conservation laws with stochastic forcing
By Arnaud Debussche, Julien Vovelle. 2013
63 citations recorded by the source corpus.
Under an hypothesis of non-degeneracy of the flux, we study the long-time behaviour of periodic scalar first-order conservation laws with stochastic forcing in any space dimension. For sub-cubic fluxes, we show the existence of an invariant measure. Moreover for sub-quadratic fluxes we show uniqueness and ergodicity of the invariant measure. Also, since this invariant measure is supported by $$L^p$$Lp for some $$p$$p small, we are led to generalize to the stochastic case the theory of $$L^1$$L1 solutions developed by Chen and Perthame (Ann Inst H Poincaré Anal Non Linéaire 20(4):645–668, 2003).
Subfields: Applied Mathematics, Computational Mechanics, Finance
View Paper: https://www.semanticscholar.org/paper/cc61a3766478fc9b80570db88fd4b0b5461de98f
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In Applied Mathematics
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- Benjamin Gess
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In Computational Mechanics
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- Panagiotis E. Souganidis
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In Finance
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- A. Deya
- Benjamin Gess
- Massimiliano Gubinelli
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- Xiangchan Zhu
- Rongchan Zhu
Citations in the corpus
- Long‐Time Behavior, Invariant Measures, and Regularizing Effects for Stochastic Scalar Conservation Laws (2014, methodology): “Instead, here we use only Fourier transforms with respect to the space variable x, a technique developed in Bouchut and Desvillettes [8] and used in Debussche and Vovelle [20] as well as in [41].”
- Global-in-time probabilistically strong and Markov solutions to stochastic 3D Navier–Stokes equations: Existence and nonuniqueness (2021, background): “According to Lemma 9 in [DV15] we know ‖z(t)‖L∞ = ‖eu0‖L∞ .”
- A priori estimates for rough PDEs with application to rough conservation laws (2016, background): “This direction also appears in several works on stochastic conservation laws and degenerate parabolic SPDEs, see [12], [15], [13], [14], [42], [41] and in the (rough) pathwise works [30], [29], [43], [50], [52].”