20,016 reputation
357138
bio website umpa.ens-lyon.fr/~serre
location Lyon, FRANCE
age 60
visits member for 5 years
seen 16 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.


1d
comment Matrix equation $XAXBXC=I$
A question about the solution of the quadratic equation. How do you define the square root ? This is an important issue, because in order that $A^*(AB^*)^{1/2}$ be a solution, it seems that we need to apply twice the identity $f(MN)M=Mf(NM)$, which requires some assumption about $f$ (here the square root) and the spectrum of teh matrices at stake.
Aug
27
awarded  Necromancer
Aug
26
awarded  Yearling
Aug
21
awarded  Necromancer
Aug
21
revised Examples of unexpected mathematical images
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Aug
20
revised Examples of unexpected mathematical images
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Aug
20
answered Examples of unexpected mathematical images
Aug
14
awarded  Nice Question
Aug
14
revised Between Fermat's primes and the twin primes
added 177 characters in body
Aug
12
revised Between Fermat's primes and the twin primes
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Aug
12
asked Between Fermat's primes and the twin primes
Aug
11
comment Generalizing a problem to make it easier
I support Fedor's comment. Your proof is unnecessarily complicated. Actually, this remains true whenever the entries are odd integers.
Aug
11
answered Generalizing a problem to make it easier
Aug
7
answered Bounded input Bounded output stability for heat equation
Aug
7
revised The conjugacy classes of diagonalizable $2 \times 2$ matrices can be identified with their eigenvalues, what about pairs?
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Aug
6
answered The conjugacy classes of diagonalizable $2 \times 2$ matrices can be identified with their eigenvalues, what about pairs?
Aug
3
comment the inverse for the trace theorem
One denomination is Babitch inverse
Aug
3
comment the inverse for the trace theorem
@37238. When $\Omega$ is a half-space, just make a Fourier transform in the variables tangent to the boundary. Then you build by hand the inverse.
Jul
31
comment Not especially famous, long-open problems which anyone can understand
@AndreasThom. Not yet.
Jul
31
comment Not especially famous, long-open problems which anyone can understand
@Andreas. Strange that this paper deals only with $k={\mathbb C}$.