Singularity Formation in the Deterministic and Stochastic Fractional Burgers Equation

@article{Ramirez2022SingularityFI,
  title={Singularity Formation in the Deterministic and Stochastic Fractional Burgers Equation},
  author={Elkin Ram'irez and Bartosz Protas},
  journal={ArXiv},
  year={2022},
  volume={abs/2104.10759}
}
Systematic search for extreme and singular behaviour in some fundamental models of fluid mechanics
  • B. Protas
  • Mathematics
    Philosophical Transactions of the Royal Society A
  • 2022
This review article offers a survey of the research program focused on a systematic computational search for extreme and potentially singular behaviour in hydrodynamic models motivated by open

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Motivated by the results concerning the regularity of solutions to the fractional Navier-Stokes system and questions about the influence of noise on the formation of singularities in hydrodynamic
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This study considers the problem of the extreme behavior exhibited by solutions to Burgers equation subject to stochastic forcing. More specifically, we are interested in the maximum growth achieved
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We consider the Langevin equation describing a non-viscous Burgers fluid stochastically perturbed by uniform noise. We introduce a deterministic function that corresponds to the mean of the velocity
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TLDR
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It is well known that the solutions to the non-viscous Burgers equation develop a gradient catastrophe at a critical time provided the initial data have a negative derivative in certain points. We
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