Yan Guo, Walter Strauss, and I organized two special issues on Nonlinear Waves and Kinetic Theory dedicated to the memory of Bob Glassey, who sadly passed away recently (I wrote an eulogy of his passing on this blog). The special issues are now published on the Kinetic and Related Models journal, Issue 1 and Issue 2.

Here are excerpts from our preface:

Bob Glassey was an extraordinary mathematician.  In spite of his modesty, his work has been greatly admired and he was personally well-liked by everyone. 

Bob’s early work concerned the asymptotic properties of waves, including the Maxwell-Dirac system of quantum electrodynamics, at a time when the whole subject was still at a fairly primitive stage.  A much-quoted key discovery in 1977 was his proof of blow-up of the nonlinear Schrodinger equations that model the focusing of laser beams.  It was the first such proof and it predated subsequent work by many other researchers.  Several of his papers on the Minkowski Yang-Mills equations established the asymptotic behavior of finite-energy solutions, such as local energy decay and scattering properties, as a consequence of the equations’ conformal invariance.  

Beginning in the 1980’s Bob focused his attention on the Vlasov-Maxwell system (VM), which models the dynamics of plasmas.  His results on its existence theory were groundbreaking at the time and are still today the definitive results on the subject. The fundamental 1986 paper with W. Strauss established that, for the relativistic VM system, singularities can occur only due to to the particles that travel at relativistically high velocities.  He and J. Schaeffer proved that the particles in almost neutral plasmas in 3D cannot speed up too fast, which therefore implied global existence. Then in a truly profound paper in 1998 they proved that the system is globally well-posed for the two-dimensional relativistic VM.  It follows that the same is true for the 2.5-dimensional problem. The 3D problem is still unsolved after multiple attempts by many mathematicians.  

Together with J. Schaeffer, Bob pioneered the mathematical study of Landau damping for the Vlasov-Poisson equation. In particular, their surprising 1995 paper proved that Landau damping for an unconfined plasma is sensitive to the background electrons: the faster some particles travel, the slower is the decay of the electric field. They also showed that there is no Landau damping when the background electron distribution is compactly supported. Several of his papers after 1993 concern models with collisions:  the relativistic Boltzmann equation and the Vlasov-Boltzmann system near a Maxwellian equilibrium. 

Bob’s book, “The Cauchy Problem in Kinetic Theory”, is the classic book on the subject, including both collisional and collisionless systems, a beautiful exposition that has been the standard reference for subsequent generations of researchers. 

Bob was a warm and supportive colleague who greatly influenced a generation of young people in kinetic theory.  He was an avid squash player and a lover of jazz, as well as  being very devoted to his family.  We will miss him dearly. This special volume is dedicated to his memory.