139 citations · 562 across the 42 of their papers we have counts for
51 papers
Stability threshold of nearly-Couette shear flows with Navier boundary conditions in 2D
Jacob Bedrossian, Siming He, Sameer Iyer +1
In this work, we prove a threshold theorem for the 2D Navier-Stokes equations posed on the periodic channel, , supplemented with Navier boundary condition…
Non-invariance of Gaussian Measures under the 2D Euler Flow
Jacob Bedrossian, Mickaël Latocca
In this article we consider the two-dimensional incompressible Euler equations and give a sufficient condition on Gaussian measures of jointly independent Fourier coefficients supp…
A note on cascade flux laws for the stochastically-driven nonlinear Schrödinger equation
Jacob Bedrossian
In this note we point out some simple sufficient (plausible) conditions for `turbulence' cascades in suitable limits of damped, stochastically-driven nonlinear Schrödinger equation…
A brief introduction to the mathematics of Landau damping
Jacob Bedrossian
In these short, rather informal, expository notes I review the current state of the field regarding the mathematics of Landau damping, based on lectures given at the CIRM Research…
Taylor dispersion and phase mixing in the non-cutoff Boltzmann equation on the whole space
Jacob Bedrossian, Michele Coti Zelati, Michele Dolce
In this paper, we describe the long-time behavior of the non-cutoff Boltzmann equation with soft potentials near a global Maxwellian background on the whole space in the weakly col…
The Vlasov-Poisson and Vlasov-Poisson-Fokker-Planck systems in stochastic electromagnetic fields: local well-posedness
Jacob Bedrossian, Stavros Papathanasiou
In this paper, we construct unique, local-in-time strong solutions to the Vlasov-Poisson (VP) and Vlasov-Poisson-Fokker-Planck (VPFP) systems subjected to external, spatially regul…
Stationary measures for stochastic differential equations with degenerate damping
Jacob Bedrossian, Kyle Liss
A variety of physical phenomena involve the nonlinear transfer of energy from weakly damped modes subjected to external forcing to other modes which are more heavily damped. In thi…
Lower bounds on the Lyapunov exponents of stochastic differential equations
Jacob Bedrossian, Alex Blumenthal, Sam Punshon-Smith
In this article, we review our recently introduced methods for obtaining strictly positive lower bounds on the top Lyapunov exponent of high-dimensional, stochastic differential eq…
Chaos in stochastic 2d Galerkin-Navier-Stokes
Jacob Bedrossian, Sam Punshon-Smith
We prove that all Galerkin truncations of the 2d stochastic Navier-Stokes equations in vorticity form on any rectangular torus subjected to hypoelliptic, additive stochastic forcin…
Non-existence of some approximately self-similar singularities for the Landau, Vlasov-Poisson-Landau, and Boltzmann equations
Jacob Bedrossian, Maria Pia Gualdani, Stanley Snelson
We consider the homogeneous and inhomogeneous Landau equation for very soft and Coulomb potentials and show that approximate Type I self-similar blow-up solutions do not exist unde…
Nonlinear inviscid damping and shear-buoyancy instability in the two-dimensional Boussinesq equations
Jacob Bedrossian, Roberta Bianchini, Michele Coti Zelati +1
We investigate the long-time properties of the two-dimensional inviscid Boussinesq equations near a stably stratified Couette flow, for an initial Gevrey perturbation of size $\var…
Encoded Prior Sliced Wasserstein AutoEncoder for learning latent manifold representations
Sanjukta Krishnagopal, Jacob Bedrossian
While variational autoencoders have been successful in several tasks, the use of conventional priors are limited in their ability to encode the underlying structure of input data.…
Quantitative spectral gaps and uniform lower bounds in the small noise limit for Markov semigroups generated by hypoelliptic stochastic differential equations
Jacob Bedrossian, Kyle Liss
We study the convergence rate to equilibrium for a family of Markov semigroups generated by a class of hypoelliptic stochastic differential equations o…
Linearized wave-damping structure of Vlasov-Poisson in
Jacob Bedrossian, Nader Masmoudi, Clement Mouhot
In this paper we study the linearized Vlasov-Poisson equation for localized disturbances of an infinite, homogeneous Maxwellian background distribution in $\mathbb R^3_x \times \ma…
A regularity method for lower bounds on the Lyapunov exponent for stochastic differential equations
Jacob Bedrossian, Alex Blumenthal, Sam Punshon-Smith
We put forward a new method for obtaining quantitative lower bounds on the top Lyapunov exponent of stochastic differential equations (SDEs). Our method combines (i) an (apparently…
Uniqueness Criteria for the Oseen Vortex in the 3d Navier-Stokes Equations
Jacob Bedrossian, William Golding
In this paper, we consider the uniqueness of solutions to the 3d Navier-Stokes equations with initial vorticity given by , where is the one d…
Almost-sure enhanced dissipation and uniform-in-diffusivity exponential mixing for advection-diffusion by stochastic Navier-Stokes
Jacob Bedrossian, Alex Blumenthal, Samuel Punshon-Smith
We study the mixing and dissipation properties of the advection-diffusion equation with diffusivity and advection by a class of random velocity fields on …
The Batchelor spectrum of passive scalar turbulence in stochastic fluid mechanics at fixed Reynolds number
Jacob Bedrossian, Alex Blumenthal, Sam Punshon-Smith
In 1959, Batchelor predicted that the stationary statistics of passive scalars advected in fluids with small diffusivity should display a power spectrum along an ine…
Inviscid damping and enhanced dissipation of the boundary layer for 2D Navier-Stokes linearized around Couette flow in a channel
Jacob Bedrossian, Siming He
We study the 2D Navier-Stokes equations linearized around the Couette flow in the periodic channel with no-slip boundary conditions in the vanis…
Almost-sure exponential mixing of passive scalars by the stochastic Navier-Stokes equations
Jacob Bedrossian, Alex Blumenthal, Samuel Punshon-Smith
We deduce almost-sure exponentially fast mixing of passive scalars advected by solutions of the stochastically-forced 2D Navier-Stokes equations and 3D hyper-viscous Navier-Stokes…
Sufficient conditions for dual cascade flux laws in the stochastic 2d Navier-Stokes equations
Jacob Bedrossian, Michele Coti Zelati, Sam Punshon-Smith +1
We provide sufficient conditions for mathematically rigorous proofs of the third order universal laws capturing the energy flux to large scales and enstrophy flux to small scales f…
Lagrangian chaos and scalar advection in stochastic fluid mechanics
Jacob Bedrossian, Alex Blumenthal, Samuel Punshon-Smith
We study the Lagrangian flow associated to velocity fields arising from various models of fluid mechanics subject to white-in-time, -in-space stochastic forcing in a periodic…
Vortex filament solutions of the Navier-Stokes equations
Jacob Bedrossian, Pierre Germain, Benjamin Harrop-Griffiths
We consider solutions of the Navier-Stokes equations in with vortex filament initial data of arbitrary circulation, that is, initial vorticity given by a divergence-free vecto…
The linearized Vlasov and Vlasov-Fokker-Planck equations in a uniform magnetic field
Jacob Bedrossian, Fei Wang
We study the linearized Vlasov equations and the linearized Vlasov-Fokker-Planck equations in the weakly collisional limit in a uniform magnetic field. In both cases, we consider p…