bio  website  umpa.enslyon.fr/~serre 

location  Lyon, FRANCE  
age  60  
visits  member for  4 years, 9 months 
seen  1 hour ago  
stats  profile views  11,337 
My research activity is mainly in PDEs, with applications to Physics, especially in Fluid Dynamics. I have written a 2volume book on Conservation laws, and a book about the Hyperbolic IBVP (in collaboration with S. BenzoniGavage). I have edited in collaboration with S. Friedlander, a 4volume 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
added 31 characters in body 
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 Diteslui, in La GrandeDuchesse 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 BorelCantelli 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
added 87 characters in body 
Apr 10 
answered  Rigorous justification that overdetermined systems do not have a solution 