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 !+ Continue reading
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.+ Continue reading
Hung Tran and I are organizing a summer school on "PDEs and Applied Mathematics" at Vietnam Institute for Advanced Study in Mathematics in Hanoi, Vietnam, July 14-25, 2014. The summer school will include five main lecture series by David Gerard-Varet (Paris 7), Hiroyoshi Mitake (Hiroshima), Toan Nguyen (Penn State), Hung Tran (Chicago), and Kevin Zumbrun (Indiana), of about five to eight hours each, that will be aimed at the level of advanced undergraduate students, graduate students, and postdocs. All lectures are in the mornings, leaving the afternoons open for discussions. There will be a one-day workshop in which several participants will deliver short research talks. More details can be found at the VIASM institute's webpage.
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