Propagation of Moments and Semiclassical Limit from Hartree to Vlasov Equation

Laflèche, Laurent

doi:10.1007/s10955-019-02356-7

Cited by 33 publications

(46 citation statements)

References 52 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Besides providing the best-known uniqueness criterion for Vlasov-Poisson, this approach also gives a new proof of uniqueness à la Yudovich for 2D Euler. Loeper's result has been generalized to less singular kernels [37], and it is the cornerstone for several other stability arguments [7,14,36,42,44,48,58]. Also, Loeper's uniqueness criterion for Vlasov-Poisson has been extended to solutions whose associated density belongs to some suitable Orlicz spaces [38,51].…”

Section: General Overviewmentioning

confidence: 99%

A New Perspective on Wasserstein Distances for Kinetic Problems

Iacobelli

2022

Arch Rational Mech Anal

View full text Add to dashboard Cite

We introduce a new class of Wasserstein-type distances specifically designed to tackle questions concerning stability and convergence to equilibria for kinetic equations. Thanks to these new distances, we improve some classical estimates by Loeper (J Math Pures Appl (9) 86(1):68–79, 2006) and Dobrushin (Funktsional Anal i Prilozhen 13:48–58, 1979) on Vlasov-type equations, and we present an application to quasi-neutral limits.

show abstract

Section: General Overviewmentioning

confidence: 99%

A New Perspective on Wasserstein Distances for Kinetic Problems

Iacobelli

2022

Arch Rational Mech Anal

View full text Add to dashboard Cite

show abstract

“…However to the best of the authors' knowledge, its generalization to a general Riesz interaction kernel a ∈ (0, d) is a novelty. A similar technique can be found in [22]. Since this observation is crucial with respect to the competition between diffusion and aggregation, we detail the proof.…”

Section: Tightness and Couplingmentioning

confidence: 84%

Fractional Keller–Segel equation: Global well-posedness and finite time blow-up

Laflèche

Salem

2019

Communications in Mathematical Sciences

Self Cite

View full text Add to dashboard Cite

This article studies the aggregation diffusion equationwhere ∆ α 2 denotes the fractional Laplacian and K = x |x| a is an attractive kernel. This equation is a generalization of the classical Keller-Segel equation, which arises in the modeling of the motion of cells. In the diffusion dominated case a < α we prove global well-posedness for an L 1 k initial condition, and in the fair competition case a = α for an L 1 k ∩ L ln L initial condition. In the aggregation dominated case a > α, we prove global or local well posedness for an L p initial condition, depending on some smallness condition on the L p norm of the initial condition. We also prove that finite time blow-up of even solutions occurs, under some initial mass concentration criteria.

show abstract

“…In the recent development, the convergence to Vlasov equation in the semiclassical Wasserstein pseudo-distance has been proved in [23][24][25]28,29]. The semiclassical Wasserstein pseudo-distance is computed between the Husimi measure and Vlasov solution.…”

Section: Introductionmentioning

confidence: 99%

Combined Mean-Field and Semiclassical Limits of Large Fermionic Systems

2021

View full text Add to dashboard Cite

We study the time dependent Schrödinger equation for large spinless fermions with the semiclassical scale $$\hbar = N^{-1/3}$$ ħ = N - 1 / 3 in three dimensions. By using the Husimi measure defined by coherent states, we rewrite the Schrödinger equation into a BBGKY type of hierarchy for the k particle Husimi measure. Further estimates are derived to obtain the weak compactness of the Husimi measure, and in addition uniform estimates for the remainder terms in the hierarchy are derived in order to show that in the semiclassical regime the weak limit of the Husimi measure is exactly the solution of the Vlasov equation.

show abstract

Propagation of Moments and Semiclassical Limit from Hartree to Vlasov Equation

Cited by 33 publications

References 52 publications

A New Perspective on Wasserstein Distances for Kinetic Problems

A New Perspective on Wasserstein Distances for Kinetic Problems

Fractional Keller–Segel equation: Global well-posedness and finite time blow-up

Combined Mean-Field and Semiclassical Limits of Large Fermionic Systems

Contact Info

Product

Resources

About