What's new

NEW paper: Spectral Instability of Symmetric Shear Flows in a Two-dimensional Channel

Feb 6, 2014: I've just uploaded a new paper on arXiv 1402.1395 with E. Grenier (ENS Lyon) and Y. Guo (Brown). This paper concerns spectral instability of shear flows in the incompressible Navier-Stokes equations with sufficiently large Reynolds number: $R\to \infty$. It is well-documented in the physical literature, going back to Heisenberg, C.C. Lin, Tollmien, Drazin and Reid, that generic plane shear profiles other than the linear Couette flow are linearly unstable for sufficiently large Reynolds number. In this work, we provide a complete mathematical proof of these physical results.

Check out also my talk at Brown on the subject !

Full Summer Program on "PDEs and Applied Math" at VIASM, July 14 - Aug 7, 2014

This summer program includes several short courses and workshops that will be aimed at the level of advanced undergraduate students, graduate students and postdocs. Most lectures are in the mornings, leaving the afternoons open for discussions. Our primarily goal is to attract young and talented researchers to work in PDEs, and to build up a network between scientists in Vietnam and abroad.