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UID:1145@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20160322T110000
DTEND;TZID=Europe/Paris:20160322T120000
DTSTAMP:20160307T100000Z
URL:https://www.i2m.univ-amu.fr/evenements/metastability-and-time-delayed-
 instabilities-in-hydrodynamical-equations/
SUMMARY: (...): Metastability and time delayed instabilities in hydrodynami
 cal equations
DESCRIPTION:: In this talk I will describe two phenomena arising in the stu
 dy of the long time dynamics of solutions to different classes of PDEs\, a
 mong which we include PDEs emerging in fluid dynamics.The first phenomenon
  is known as metastable dynamics and appears when solutions exhibit a firs
 t time scale (usually of order O(1)) in which they are close to some unsta
 ble configuration\, before converging to their asymptotic limit in an expo
 nentially long time.We then focus on the influence of the viscosity in hyd
 rodynamical equations: given a strongly unstable PDE\, a small viscous ter
 m introduces a time delay in the instability (that is\, we observe the sol
 utions to have a linear growth in time before exhibiting an exponential gr
 owth).These two phenomena have in common the fact that the solutions of th
 e equation under consideration exhibit a certain stable (observable) behav
 ior for a long time interval before they : - 1. converge to the asymptotic
  limit in the case of a metastable behavior\;- 2. experience an exponentia
 l growth in time in the case of a time-delayedinstability.Some of these re
 sults have been obtained in collaboration with Corrado Mascia (Università
  di Roma La Sapienza) and Benjamin Texier (Université Paris Diderot\, IMJ
 -PRG).https://sites.google.com/site/martastranihomepage/
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