A Vlasov equation with Dirac potential used in fusion plasmas

作者：Bardos Claude^*; Nouri Anne

来源：Journal of Mathematical Physics, 2012, 53(11): 115621.

DOI：10.1063/1.4765338

• Hadamard matrices
• initial value problems
• nonlinear equations
• plasma density
• plasma nonlinear processes
• plasma transport processes
• Vlasov equation

Well-posedness of the Cauchy problem is analyzed for a singular Vlasov equation governing the evolution of the ionic distribution function of a quasineutral fusion plasma. The Penrose criterium is adapted to the linearized problem around a time and space homogeneous distribution function showing (due to the singularity) more drastic differences between stable and unstable situations. This pathology appears on the full nonlinear problem, well-posed locally in time with analytic initial data, but generally ill-posed in the Hadamard sense. Eventually with a very different class of solutions, mono-kinetic, which constrains the structure of the density distribution, the problem becomes locally in time well-posed.

• 出版日期2012-11