Travauxbis de Christophe Cheverry

Research in

Mathematical Physics and

Partial Differential Equations

I am working on mathematical questions which are related to the understanding of wave
particle interactions in Plasma Physics, nuclear magnetic resonance, Quantum Mechanics,
Particle Physics or Fluid Dynamics.

Preprints and works accepted for publication:

C. Cheverry and S. Ibrahim, The relativistic Vlasov-Maxwell system: local smooth solvability for weak topologies, preprint, (2023).

C. Cheverry and S. Farhat, Long time gyrokinetic equations, 40 p., to appear in
Quarterly of Applied Mathematics (2023).

Recent research works.

C. Cheverry and S. Farhat, A paradigm for the creation of scales and phases in nonlinear evolution equations, Electronic Journal of Differential Equations, No. 9, 59 p. (2023).

R. Carles and C. Cheverry, Turbulent effects through quasi-rectification, 105 p.,
Mémoires de la Société de France, No 174 (2022).

C. Cheverry, S. Ibrahim and D. Preissl, Uniform Lifetime for Classical Solutions to the Hot, Magnetized, Relativistic Vlasov Maxwell System, 45 p., Kinetic & Related Models, 14 (2021), No 6, 1035-1079.

C. Cheverry and N. Raymond, A Guide to Spectral Theory, Applications and Exercises,
Birkhäuser, Advanced Texts: Basler LehrBäucher, (2021), 258 p..

C. Cheverry and S. Ibrahim, The relativistic Vlasov Maxwell equations for strongly magnetized plasmas,
Communications in Mathematical Sciences, 18 (2020), no. 1, 123-162.

C. Cheverry, Mathematical perspectives in plasma turbulence, Research and Reports on Mathematics,
2018, 2:2.

The focus of my recent contributions is put on the study of chorus waves. Chorus waves are beautiful songs
which are sung by all stellar and planetary magnetospheres. In the case of the Earth (dipole model for the
external magnetic field), they are called the dawn chorus. This electromagnetic intermittency phenomenon
can be triggered by trapped electron mode turbulence. It is based on a mechanism of wave-particle interaction.
It still hold many mysteries. Some mathematical interpretation has just been given in the publication:

C. Cheverry, Can one hear whistler waves ? Comm. Math. Phys., No. 338, 2015, 641 - 703.

In the case of collisionless axisymmetric plasmas immersed in a strong magnetic field, the turbulent transport
can also be described through a deterministic approach, see the preprint:

C. Cheverry Anomalous transport, Journal of Differential Equations, Vol. 262, Number 3, 2017, 2987 - 3033,
with some few precisions.

Chorus emissions are coming from a mesoscopic caustic effect due to the crossing in the cotangent bundle
of two geometrical objects. The first is the trace at mirror points of a Lagrangian submanifold issued from
the long time dynamics of charged particles. The second is the characteristic variety that is associated to the
relativistic Vlasov-Maxwell equations, see the article:

C. Cheverry and A. Fontaine, Dispersion relations in cold magnetized plasmas, Kinetic and Related Models,
Vol 10, Issue 2, June 2017, 373--421.

and see the preprint:

C. Cheverry and A. Fontaine, Dispersion relations in hot magnetized plasmas, Journal of Mathematical Analysis and Applications, Vol. 466, Issue 2, October 2018, 1238--1280.

In the presence of a strong magnetic field, the characteristic variety sustaining electromagnetic wave propagation may reveal surprising aspects.
As a matter of fact, an oscillating wave with time frequency τ and space frequency ξ can persist if and only if τ is related to ξ by a dispersion
relation. When the value of τ is fixed below the resonance frequencies, the direction ξ must belong to cones:

By contrast, when τ is fixed above the cutoff frequencies, the direction ξ must belong to two nested spheres which collapse when τ becomes large.
Asymptotically, we recover spherical waves:

Past publications. Some selection is available on MathScinet , ZentralBlatt MATH and Google Scholar. A complete list can be found at the
following address.