|
Date Time |
Location | Speaker |
Title – click for abstract |
 |
01/17 3:00pm |
Zoom |
Abdon Moutinho Université Paris 13 |
Dynamics of two interacting kinks for the phi6 model
We consider the $\phi^6$ model given by the one-dimensional nonlinear wave
equation $\partial_t^2 \phi - \partial_x^2 \phi + 2 \phi - 8 \phi^3 + 6 \phi^5 = 0$. In this talk, we will describe the long time behavior of all the solu-
tions of this partial differential equation satisfying the boundary condition
$\lim_{x \to \infty} \phi(t,x) = 1$, $\lim_{x \to -\infty} \phi(t,x) = -1$ and having energy slightly larger than the minimum possible. Indeed, we will also show that this set of solutions can be written explicitly as a sum of two moving kinks (topological solitons) with a remainder with low energy norm. Our estimate for the energy norm of the remainder is close to the optimal during the large time interval we study. |
 |
01/24 3:00pm |
BLOC 302 |
Benjamin Dodson Johns Hopkins University |
Rigidity for the one dimensional, quintic nonlinear Schrodinger equation
In this talk, we prove rigidity for the one dimensional, quintic nonlinear Schrodinger equation with mass equal to the mass of the soliton. We prove that non-scattering solutions are either the soliton or a pseudoconformal transformation of the soliton. |
 |
02/14 3:00pm |
BLOC 302 |
Graham Cox Memorial University of Newfoundland |
Turing instability via the generalized Maslov index
TBA |
 |
02/21 3:00pm |
BLOC 302 |
Luan Hoang Texas Tech University |
Complicated asymptotic expansions for the Navier-Stokes equations
The long-time behavior of solutions of the three-dimensional Navier-Stokes equations in a periodic domain is studied. The time-dependent body force decays, as time $t$ tends to infinity, in a complicated but coherent manner. In fact, it is assumed to have a general and complicated asymptotic expansion which involves complex powers of $e^t$, $t$, $\ln t$, or other iterated logarithmic functions of $t$. We prove that all Leray-Hopf weak solutions admit an asymptotic expansion which is independent of the solutions and is uniquely determined by the asymptotic expansion of the body force. The proof makes use of the complexifications of the Gevrey-Sobolev spaces together with those of the Stokes operator and the bilinear form of the Navier-Stokes equations.
|
 |
03/21 3:00pm |
BLOC 302 |
Xin Liu Texas A&M University |
A revisit to the rigorous justification of the quasi-geostrophic approximation
TBA |
 |
03/28 3:00pm |
BLOC 302 |
Boualem Khouider University of Vicotria |
TBA
TBA |
 |
04/04 3:00pm |
BLOC 302 |
Christos Mantoulidis Rice University |
TBA
TBA |
 |
04/25 3:00pm |
BLOC 302 |
Juhi Jang University of Southern California |
TBA
TBA |