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Vacuum states in hydrodynamic models.

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HYD2 - Dispersive hydrodynamics: mathematics, simulation and experiments, with applications in nonlinear waves

Vacuum or “dry” states, whereby density-like variables of hydrodynamic models vanish on sets of initial conditions, can cause development of finite time singularities in the evolution of model solutions. This loss of regularity in the ensuing evolution poses challenges from both the analytical and numerical standpoint.  This talk will discuss a selected class of examples where a finite-time singularity can be “unfolded” in appropriately defined variables, and how the local and global evolution of solutions, in either weak or strong form, can thus be recovered and continued past the singularity time. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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