Well-posedness of one-dimensional Korteweg models.
Well-posedness of the Euler and Navier-Stokes equations in the Lebesque spaces Lsp(R2).
In this paper we show that the Euler equation for incompressible fluids in R2 is well posed in the (vector-valued) Lebesgue spacesLsp = (1 - ∆)-s/2 Lp(R2) with s > 1 + 2/p, 1 < p < ∞and that the same is true of the Navier-Stokes equation uniformly in the viscosity ν.
Weyl formula with optimal remainder estimate of some elastic networks and applications
We consider a network of vibrating elastic strings and Euler-Bernoulli beams. Using a generalized Poisson formula and some Tauberian theorem, we give a Weyl formula with optimal remainder estimate. As a consequence we prove some observability and stabilization results.
Whitney elements on pyramids.
Wigner series and (semi)classical limits with periodic potentials
WKB analysis for the Gross-Pitaevskii equation with non-trivial boundary conditions at infinity