19,285 reputation
352134
bio website umpa.ens-lyon.fr/~serre
location Lyon, FRANCE
age 60
visits member for 4 years, 9 months
seen 1 hour 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.


2d
revised John Nash's Mathematical Legacy
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2d
revised John Nash's Mathematical Legacy
added 264 characters in body
May
25
awarded  Nice Answer
May
24
answered John Nash's Mathematical Legacy
May
24
awarded  Enlightened
May
24
awarded  Nice Answer
May
23
awarded  Good Answer
May
21
comment Resolvent estimate of hyperbolic Laplacian
The proof is analogous to the Euclidian case.
May
15
answered Weak solutions for a PDE of fourth order
May
12
comment What is the trace of this operator in $L^\infty$ (if this question make sense)?
Suppose $f\equiv1$. Then $A_f$ is the identity over an infinite dimensional space. Its trace should be infinite.
May
12
comment Least collaborative mathematician
En attendant Godeaux ...
May
6
answered Examples of eventual counterexamples
May
5
answered Analogue of Cayley Hamilton theorem for operators on Hilbert space
May
4
awarded  Popular Question
Apr
27
comment How has modern algebraic geometry affected other areas of math?
Sometimes, "I have a friend who ..." is the pretext for being allowed to say something one really thinks. I have in mind the famous aria Dites-lui, in La Grande-Duchesse de Gerolstein. Are you that friend ?
Apr
22
revised Proofs of the uncountability of the reals.
added 4 characters in body
Apr
19
comment When has the Borel-Cantelli heuristic been wrong?
If $n\ge2$, the argument gives $p=k2^{n+2}+1$. For this, use the fact that $2$ is a square imod $p$. This can be used to detect the first factor of $F_5$. It is a prime number of the form $k2^7+1$. But $k\ne1,3,4$ (not prime) $k\ne2$ (because another $F_m$ cannot be a factor). So the first candidate is $5\cdot128+1=641$, a factor found by Euler.
Apr
15
awarded  Nice Answer
Apr
10
revised Rigorous justification that overdetermined systems do not have a solution
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Apr
10
answered Rigorous justification that overdetermined systems do not have a solution