KRM
Non-existence and non-uniqueness for multidimensional sticky particle systems
Alberto Bressan Truyen Nguyen
The paper is concerned with sticky weak solutions to the equations of pressureless gases in two or more space dimensions. Various initial data are constructed, showing that the Cauchy problem can have (i) two distinct sticky solutions, or (ii) no sticky solution, not even locally in time. In both cases the initial density is smooth with compact support, while the initial velocity field is continuous.
keywords: non-uniqueness Sticky particle systems non-existence conservation laws. pressureless Euler system
KRM
Erratum to: Global magnetic confinement for the 1.5D Vlasov-Maxwell system
Toan T. Nguyen Truyen V. Nguyen Walter A. Strauss
N/A
keywords: global smooth solution boundary conditions. magnetic confinement Vlasov-Maxwell system
KRM
Global magnetic confinement for the 1.5D Vlasov-Maxwell system
Toan T. Nguyen Truyen V. Nguyen Walter A. Strauss
We establish the global-in-time existence and uniqueness of classical solutions to the ``one and one-half'' dimensional relativistic Vlasov--Maxwell systems in a bounded interval, subject to an external magnetic field which is infinitely large at the spatial boundary. We prove that the large external magnetic field confines the particles to a compact set away from the boundary. This excludes the known singularities that typically occur due to particles that repeatedly bounce off the boundary. In addition to the confinement, we follow the techniques introduced by Glassey and Schaeffer, who studied the Cauchy problem without boundaries.
keywords: magnetic confinement global smooth solution Vlasov-Maxwell system boundary conditions.

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