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KRM

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.

KRM

N/A

KRM

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.

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