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SUMMARY:Vacuum states in hydrodynamic models. - Roberto Camassa (Universit
 y of North Carolina)
DTSTART:20220727T143000Z
DTEND:20220727T153000Z
UID:TALK176804@talks.cam.ac.uk
DESCRIPTION:Vacuum or &ldquo\;dry&rdquo\; states\, whereby density-like va
 riables of hydrodynamic models vanish on sets of initial conditions\, can 
 cause development of finite time singularities in the evolution of model s
 olutions. This loss of regularity in the ensuing evolution poses challenge
 s from both the analytical and numerical standpoint.&nbsp\;\nThis talk wil
 l discuss a selected class of examples where a finite-time singularity can
  be &ldquo\;unfolded&rdquo\; in appropriately defined variables\, and how 
 the local and global evolution of solutions\, in either weak or strong for
 m\, can thus be recovered and continued past the singularity time.&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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