18,491 reputation
249129
bio website umpa.ens-lyon.fr/~serre
location Lyon, FRANCE
age 60
visits member for 4 years, 5 months
seen 3 hours ago

My research activity is mainly in PDEs, with applications to Physics, especially in Fluid Dynamics. I have written a 2-volume book on Conservation laws, and a book about the Hyperbolic IBVP (in collaboration with S. Benzoni-Gavage). I have edited in collaboration with S. Friedlander, a 4-volume Handbook of Mathematical Fluid Dynamics.

I have a continuous interest in Matrix Analysis. I have written a Graduate Text about Matrices. The second edition has been released in November 2010.


8h
reviewed Close Supremum of positve kernel
8h
reviewed Close Solution to a PDE with constant data - what is the fault in my proof?
2d
answered Surjectivity of curl
2d
reviewed Close Discrete Taylor's Formula in n dimensions
2d
revised Homogeneous polynomial vector fields tangent to the unit sphere
added 30 characters in body
2d
comment Homogeneous polynomial vector fields tangent to the unit sphere
Yes indeed. I realized a bit late that it is enough to say that $v\mapsto x\wedge v\sim x\cdot v$ is onto $\Lambda_n({\mathbb R}^n)\otimes{\rm Hom}_n^{d+1}$.
2d
accepted Homogeneous polynomial vector fields tangent to the unit sphere
2d
revised Homogeneous polynomial vector fields tangent to the unit sphere
added 63 characters in body
2d
asked Homogeneous polynomial vector fields tangent to the unit sphere
Jan
29
comment Are A and A^T unitarily equivalent over a p-adic field?
Well, the field of differential equations begins with linear ones. Therefore, it needs a lot of linear algebra, and Kedlaya's book contains a thorough introduction to all kind of matrices with entries in $p$-adic fields.
Jan
29
reviewed Close Limiting Ratio of Solutions to Ordinary Differential Equations
Jan
29
reviewed Close Riemann Siegel function and gamma function
Jan
29
comment Are A and A^T unitarily equivalent over a p-adic field?
Did you look a Kedlaya's book ?
Jan
28
reviewed Leave Open Find an integrable, positive, unbounded, analytic function
Jan
27
comment positively invariant set respec to fractional system
If $f(t,M)$ is not included in $M$, there is no hope that $M$ be positively invariant. You can convince yourself by considering the ODE case ($\alpha=1$).
Jan
27
answered positively invariant set respec to fractional system
Jan
27
awarded  Enlightened
Jan
27
awarded  Nice Answer
Jan
26
reviewed Leave Open Irreducibility of a polynomial
Jan
26
comment Irreducibility of a polynomial
@Ycor. Your $g$ is not homogeneous.