# Analysis Seminar

#### On the Existence of the V-States for Some Transport Models

**Speaker:**
Zineb Hassainia, Courant

**Location:**
Warren Weaver Hall 1302

**Date:**
Thursday, October 29, 2015, 11 a.m.

**Synopsis:**

In this lecture, we shall discuss some recent results on rotating patches (also called V-states) for two dimensional transport models such as Euler equations and the generalized surface quasi-geostrophic equations. We shall first focus on the simply connected case and prove the existence of such structures in a neighborhood of Rankine vortices by using the bifurcation theory. In the second part we will deal with the doubly connected case where the patches admit only one hole. More precisely, close to a given annulus we describe this family by countable branches bifurcating from this annulus at some angular velocity related to Bessel functions.

The lecture is based on joint works with de-La Hoz, Hmidi and Mateu.