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}
}
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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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SINGULARITY FORMATION IN THE DETERMINISTIC AND STOCHASTIC FRACTIONAL BURGERS EQUATIONS SINGULARITY FORMATION IN THE DETERMINISTIC AND STOCHASTIC FRACTIONAL BURGERS EQUATIONS By ELKIN WBEIMAR RAMÍREZ, M.Sc
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…
Transient growth in stochastic Burgers flows
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…
Suppression of unbounded gradients in an SDE associated with the Burgers equation
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…
Numerical simulation of focusing stochastic nonlinear Schrödinger equations
Dynamics and condensation of complex singularities for Burgers' equation II
Spatial analyticity properties of the solution to Burgers' equation with a generic initial data are presented, following the work of Bessis and Fournier [Research Reports in Physics: Nonlinear…
Maximum Rate of Growth of Enstrophy in Solutions of the Fractional Burgers Equation
TLDR
The power-law dependence of the enstrophy rate of growth on the fractional dissipation exponent has the same global form in the subcritical, critical and parts of the supercritical regime.
Tracing complex singularities with spectral methods
Galerkin Approximations for the Stochastic Burgers Equation
TLDR
The main novelty in this article is the estimation of the difference of the finite-dimensional Galerkin approximations and of the solution of the infinite-dimensional SPDE uniformly in space, instead of the usual Hilbert space estimates in the $L^2$-topology, that were shown before.
The inviscid Burgers equation with initial data of Brownian type
The solutions to Burgers equation, in the limit of vanishing viscosity, are investigated when the initial velocity is a Brownian motion (or fractional Brownian motion) function, i.e. a Gaussian…
The non-viscous Burgers equation associated with random positions in coordinate space: a threshold for blow up behaviour
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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