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SUMMARY:Global existence for small data of the viscous Green-Naghdi equati
ons
DTSTART;VALUE=DATE-TIME:20160615T132000Z
DTEND;VALUE=DATE-TIME:20160615T135500Z
DTSTAMP;VALUE=DATE-TIME:20200811T201341Z
UID:indico-contribution-2979@indico.math.cnrs.fr
DESCRIPTION:Speakers: Dena Kazerani (Laboratoire Jacques-Louis Lions)\nWe
consider the Cauchy problem for the Green-Naghdi equations with viscosity\
, for small initial data. It is well-known that adding a second order diss
ipative term to a hyperbolic system leads to the existence of global smoot
h solutions\, once the hyperbolic system is symmetrizable and the so-calle
d Kawashima-Shizuta condition is satisfied. We first show that the Green-N
aghdi equations can be written in a symmetric form\, using the associated
Hamiltonian. This system being dispersive\, in the sense that it involves
third order derivatives\, the symmetric form is based on symmetric differe
ntial operators. Then\, we use this structure for an appropriate change of
variable to prove that adding viscosity effects through a second order te
rm leads to global existence of smooth solutions\, for small data. We also
deduce that constant solutions are asymptotically stable.\n\nhttps://indi
co.math.cnrs.fr/event/939/contributions/2979/
LOCATION: Salle de Réunion - Bâtiment M2
URL:https://indico.math.cnrs.fr/event/939/contributions/2979/
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