Bilinear virial identities and applications
نویسنده
چکیده
I’ll present some recent work with F. Planchon on bilinear virial identities for the nonlinear Schrodinger equation, which are extensions of the Morawetz interaction inequalities firstly obtained by Colliander, Keel, Staffilani, Takaoka and Tao. We recover and extend known bilinear improvements to Strichartz inequalities and provide applications to various nonlinear problems, most notably on domains with boundaries.
منابع مشابه
$n$-factorization Property of Bilinear Mappings
In this paper, we define a new concept of factorization for a bounded bilinear mapping $f:Xtimes Yto Z$, depended on a natural number $n$ and a cardinal number $kappa$; which is called $n$-factorization property of level $kappa$. Then we study the relation between $n$-factorization property of level $kappa$ for $X^*$ with respect to $f$ and automatically boundedness and $w^*$-$w^*$-continuity...
متن کاملBilinear Forms and Fierz Identities for Real Spin Representations
Given a real representation of the Clifford algebra corresponding to Rp+q with metric of signature (p, q), we demonstrate the existence of two natural bilinear forms on the space of spinors. With the Clifford action of k-forms on spinors, the bilinear forms allow us to relate two spinors with elements of the exterior algebra. From manipulations of a rank four spinorial tensor introduced in [1],...
متن کاملBilinear Fourier integral operator and its boundedness
We consider the bilinear Fourier integral operatorS(f, g)(x) =ZRdZRdei1(x,)ei2(x,)(x, , ) ˆ f()ˆg()d d,on modulation spaces. Our aim is to indicate this operator is well defined onS(Rd) and shall show the relationship between the bilinear operator and BFIO onmodulation spaces.
متن کاملun 2 00 8 MAGNETIC VIRIAL IDENTITIES , WEAK DISPERSION AND STRICHARTZ INEQUALITIES
We show a family of virial-type identities for the Schrödinger and wave equations with electromagnetic potentials. As a consequence, some weak dispersive inequalities in space dimension n ≥ 3, involving Morawetz and smoothing estimates, are proved; finally, we apply them to prove Strichartz inequalities for the wave equation with a non-trapping electromagnetic potential with almost Coulomb decay.
متن کاملJ un 2 00 8 MAGNETIC VIRIAL IDENTITIES , WEAK DISPERSION AND STRICHARTZ INEQUALITIES
We show a family of virial-type identities for the Schrödinger and wave equations with electromagnetic potentials. As a consequence, some weak dispersive inequalities in space dimension n ≥ 3, involving Morawetz and smoothing estimates, are proved; finally, we apply them to prove Strichartz inequalities for the wave equation with a non-trapping electromagnetic potential with almost Coulomb decay.
متن کامل