Analysis Seminar

Analysis Seminar - Fall 2017

 

The seminar will meet bi-weekly on Mondays at 3:30pm in 103 Centennial Hall, beginning September 25.

Title: On the fast convergence of random perturbations of the gradient flow

Abstract: We consider in  this work small random perturbations (of multiplicative noise type) of  the gradient flow. We rigorously prove that under mild conditions, when  the potential function is a Morse function with additional strong saddle condition, the perturbed gradient flow converges to the neighborhood of local minimizers in  O(ln(ε-1)) time on the average, where ε>0 is the scale of the random  perturbation. Under a change of time scale, this indicates that for the  diffusion process that approximates the stochastic gradient method, it takes (up to logarithmic factor) only a linear time  of inverse stepsize to evade from all saddle points and hence it implies  a fast convergence of its discrete--time counterpart.

Title: Almost sure scattering for the energy-critical NLS 

 Abstract: We consider the defocusing energy-critical nonlinear Schrödinger equation in four space dimensions with radial (i.e. spherically-symmetric) initial data below the energy space.  In this setting, the problem is known to be ill-posed.  Nonetheless, we can show that for suitably randomized radial initial data, one obtains global well-posedness and scattering almost surely.  This is joint work with R. Killip and M. Visan.

Title: Boundary layers for viscous incompressible flow (part I)

Abstract: Prandtl boundary  layer theory is a conundrum in mathematical fluid dynamics. In this talk, I shall give an overview of the current status on the resolution of the theory, including a positive result for a family of parallel pipe flow as well as a counter example.

Title: Boundary layers for viscous incompressible flow (part II)

Abstract: Prandtl boundary  layer theory is a conundrum in mathematical fluid dynamics. In this talk, I shall give an overview of the current status on the resolution of the theory, including a positive result for a family of parallel pipe flow as well as a counter example.

Title: TBA

Abstract: TBA


For more information about the analysis seminar, contact Dr. David Grow