19,195 reputation
350131
bio website umpa.ens-lyon.fr/~serre
location Lyon, FRANCE
age 60
visits member for 4 years, 8 months
seen 2 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.


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
added 87 characters in body
Apr
10
answered Rigorous justification that overdetermined systems do not have a solution
Apr
9
answered Symmetric matrix from a nonsymmetricc matrix
Mar
31
comment “C^0 estimate for solutions to $\Delta(u)+e^{-u} \geq 0$”
This is not a special case. All the solutions $u$ are given by this formula, for a suitable holomorphic function $f$.
Mar
31
revised “C^0 estimate for solutions to $\Delta(u)+e^{-u} \geq 0$”
added 204 characters in body
Mar
31
answered “C^0 estimate for solutions to $\Delta(u)+e^{-u} \geq 0$”
Mar
28
accepted A “quadratic” triangular inequality
Mar
27
comment A “quadratic” triangular inequality
Thanks, Fedor !
Mar
27
revised A “quadratic” triangular inequality
added 155 characters in body
Mar
27
revised A “quadratic” triangular inequality
added 435 characters in body
Mar
27
revised A “quadratic” triangular inequality
added 110 characters in body
Mar
27
asked A “quadratic” triangular inequality
Mar
20
answered Blow-Up for Semi-Linear Wave Equations
Mar
12
awarded  Popular Question
Mar
10
comment Density of smooth functions in Sobolev space, respecting nonnegative traces
Actually, a Theorem due to Stampacchia says that if $\phi$ is a Lipschit functin, then $u\mapsto\phi\circ u$ is a Lipschitz function from $W^{1,p}$ into itself. Apply this to $\phi(s)=s^+$.
Mar
4
comment Classification of PDE
@Qfwfq. Right, Schroedinger's equation is linear, but the number of independent variables is $1+3N$ where $N$ is the number of particles (electrons, protons, neutrons, ...) In practice, it is untractable by numerical schemes. For this reason, one makes approximations (density functional, Hartree-Fock, Slatter and so on), which replace it by a non-linear equation in $1+3$ variables.