We prove an abstract NashMoser implicit function theorem which, when applied to control and Cauchy problems for PDEs in Sobolev class, is sharp in terms of the loss of regularity of the solution of the problem with respect to the data. The proof is a combination of: (i) the iteration scheme by Hörmander (ARMA 1976), based on telescoping series, and very close to the original one by Nash; (ii) a suitable way of splitting series in scales of Banach spaces, inspired by a simple, clever trick used in paradifferential calculus (for example, by Métivier). As an example of application, we apply our theorem to a control and a Cauchy problem for quasilinear perturbations of KdV equations, improving the regularity of a previous result. The theorem has a fruitful application also in solving a quasiperiodic version of a transport equation, which is the first step towards the reduction to constant coefficients of the linearized operator associated to onedimensional gravity water waves. This is a joint work with Pietro Baldi.
You are here
A NashMoserHörmander implicit function theorem with applications to control and Cauchy problems for PDEs
Research Group:
Emanuele Haus
Institution:
Unina
Location:
A133
Schedule:
Tuesday, February 21, 2017  11:00
Abstract:
Openings
 Public Calls for Professors
 Temporary Professors/Researchers/Visiting Professors
 SISSA Mathematical Fellowships
 Marie SklodowskaCurie Grants
 Post Doctoral Fellowships
 PhD Scolarships
 SIS Fellowships
 Undergraduate Fellowships
 Postgraduate Fellowships
 MSc in Mathematics
 MSc in Data Science and Scientific Computing (DSSC)
 Professional Master Courses
Upcoming events

Kiyokazu Nagatomo
Vertex operator algebras whose dimensions of weight one spaces are 8 and 16
Thursday, October 17, 2019  16:00

Martin Andler
The ups and downs of the development of mathematics in France since 1870
Tuesday, October 22, 2019  10:00

Stefano Scrobogna
Stabilization of the RayleighTaylor instability of an underlying fluid layer
Tuesday, October 22, 2019  11:00

Abed Bounemoura
Positive measure of KAM tori for finitely differentiable Hamiltonians
Thursday, October 24, 2019  16:00
Today's Lectures

09:00 to 11:00

09:00 to 11:00

11:00 to 13:00

14:00 to 16:00

14:00 to 16:00

14:00 to 16:00
Recent publications

R. Feola; F. Giuliani; R. Montalto; M. Procesi,Reducibility of first order li...

F. Riva,A continuous dependence result...

A. Mola; M. Tezzele; M. Gadalla; F. Valdenazzi; D. Grassi; R. Padovan; G. Rozza,Efficient Reduction in Shape P...

C. Beltrán; K. Kozhasov,The Real Polynomial Eigenvalue...