[Seminario] Seminario CAPDE Lunes 7 de Noviembre 16hrs

Claudio Muñoz cmunoz en dim.uchile.cl
Mie Nov 2 09:28:04 CLST 2016


Estimados todos,

Este correo es para invitarlos cordialmente a una nueva sesión del seminario
 CAPDE de EDPs, a realizarse el *Lunes 7 de Noviembre, a las 4pm, en la
sala de seminarios del 5to. piso del DIM, U. de Chile*.

En esta ocasión contaremos con dos profesores invitados:

*4pm*

*Chulkwang Kwak*
*Title:*

*Fifth-order modified KdV equation*
*Abstract : *In this talk, I will briefly introduce the basic low
regularity well-posedness theory of dispersive equations, we will discuss
about the Cauchy problem of the (integrable) fifth-order modified
Korteweg-de Vries (modified KdV) equation under the periodic boundary
condition. In particular, we will observe the non-trivial resonant
phenomena of the Fourier coefficients of the solution and strong high-low
interactions in nonlinear interactions. Precisely, non-trivial cubic and
quintic resonant interactions do not admit that the nonlinear solution
behave as a linear solution, so considering the integrable equation is very
useful to study the low regularity Cauchy problem. Moreover, due to the
lack of dispersive effect, we encounter the difficulty to control the
nonlinearity via the standard way, so I will introduce the short time
function space to defeat this enemy. In conclusion, we will prove the local
well-posedness of the fifth-order modified KdV in $H^s$ for $s > 2$, via
the standard energy method, and it is the first local well-posedness result
of the periodic fifth-order KdV equation.

*4:55*

*Pausa Café*
*5:10pm*
*Nikola Kamburov*



*Title:The space of one-phase free boundary solutions in the plane*
*Abstract: *In joint work with David Jerison we study the compactness of
the space of solutions to the one-phase free boundary problem in the disk,
whose positive phase is of a fixed genus. We describe the local structure
of the free boundary and obtain rigidity estimates on its shape. Via a
correspondence due to Traizet, our results are direct counterparts to
theorems by Colding and Minicozzi for minimal surfaces.

*Próximo evento/seminario: Lunes 21 Noviembre.*

Esperando contar con su presencia
Equipo CAPDE

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