A Nonlinear Plancherel Theorem with Applications to Global Well-Posedness for the Defocusing Davey-Stewartson Equation and to the Inverse Boundary Value Problem of Calderón

We prove a Plancherel theorem for a nonlinear Fourier transform in two dimensions arising in the Inverse Scattering method for the defocusing Davey-Stewartson II equation. We then use it to prove global well-posedness and scattering in $L^2$ for defocusing DSII. This Plancherel theorem also implies global uniqueness in the inverse boundary value problem of Calder\'on in dimension $2$, for conductivities \sigma>0 with $\log \sigma \in \dot H^1$. The proof of the nonlinear Plancherel theorem includes new estimates on classical fractional integrals, as well as a new result on $L^2$-boundedness of pseudo-differential operators with non-smooth symbols, valid in all dimensions

Kinetics of Carbon Dioxide Absorption into Aqueous Solution of a Polyamine

Published in an open access journal this article is also available online at http://www.chemicalbulletin.ro/admin/articole/54742art_1(1-4).pdfInternational audienceThe absorption of CO2 into an aqueous solution with 1.45 mol/L 1, 5, 8, 12- tetraazadodecane (APEDA) polyamine has been studied at three temperature (298, 313, 333 K) in a Lewis type absorber with a constant gas- liquid interface area of (15.34 ± 0.05) x 10-4 m2. The experimental results have been interpreted using the equations derived from the two film model with the assumption that the absorption occurred in the fast pseudo- first- order kinetic regime. The results confirmed the validity of this assumption for the experimental conditions: the enhancement factor was always greater than 3. The rate constant derived from the experimental data (kov, s-1) was correlated through the Arrhenius plot (ln kov = A- B/T), and the optimal values of the constants A and B were obtained by the linear regression. The absorption of CO2 from flue gas into APEDA solution is a promising process for practical application at least from the kinetic point of view. The rate constant derived from experiments is of the same order of magnitude as that for the absorption into 2- amino- 2- methyl- 1- propanol (AMP) activated with piperazine (PZ) which was found to be the most advanced system among the published data up to now

Koszul-Tate Cohomology For an Sp(2)-Covariant Quantization of Gauge Theories with Linearly Dependent Generators

The anti-BRST transformation, in its Sp(2)-symmetric version, for the general case of any stage-reducible gauge theories is implemented in the usual BV approach. This task is accomplished not by duplicating the gauge symmetries but rather by duplicating all fields and antifields of the theory and by imposing the acyclicity of the Koszul-Tate differential. In this way the Sp(2)-covariant quantization can be realised in the standard BV approach and its equivalence with BLT quantization can be proven by a special gauge fixing procedure.Comment: 13 pages, Latex, To Be Published in International Journal of Modern Physics

On the 2d Zakharov system with L^2 Schr\"odinger data

We prove local in time well-posedness for the Zakharov system in two space dimensions with large initial data in L^2 x H^{-1/2} x H^{-3/2}. This is the space of optimal regularity in the sense that the data-to-solution map fails to be smooth at the origin for any rougher pair of spaces in the L^2-based Sobolev scale. Moreover, it is a natural space for the Cauchy problem in view of the subsonic limit equation, namely the focusing cubic nonlinear Schroedinger equation. The existence time we obtain depends only upon the corresponding norms of the initial data - a result which is false for the cubic nonlinear Schroedinger equation in dimension two - and it is optimal because Glangetas-Merle's solutions blow up at that time.Comment: 30 pages, 2 figures. Minor revision. Title has been change

Strichartz estimates on Schwarzschild black hole backgrounds

We study dispersive properties for the wave equation in the Schwarzschild space-time. The first result we obtain is a local energy estimate. This is then used, following the spirit of earlier work of Metcalfe-Tataru, in order to establish global-in-time Strichartz estimates. A considerable part of the paper is devoted to a precise analysis of solutions near the trapping region, namely the photon sphere.Comment: 44 pages; typos fixed, minor modifications in several place

Strichartz Estimates for the Vibrating Plate Equation

We study the dispersive properties of the linear vibrating plate (LVP) equation. Splitting it into two Schr\"odinger-type equations we show its close relation with the Schr\"odinger equation. Then, the homogeneous Sobolev spaces appear to be the natural setting to show Strichartz-type estimates for the LVP equation. By showing a Kato-Ponce inequality for homogeneous Sobolev spaces we prove the well-posedness of the Cauchy problem for the LVP equation with time-dependent potentials. Finally, we exhibit the sharpness of our results. This is achieved by finding a suitable solution for the stationary homogeneous vibrating plate equation.Comment: 18 pages, 4 figures, some misprints correcte

Spectral Analysis for Matrix Hamiltonian Operators

In this work, we study the spectral properties of matrix Hamiltonians generated by linearizing the nonlinear Schr\"odinger equation about soliton solutions. By a numerically assisted proof, we show that there are no embedded eigenvalues for the three dimensional cubic equation. Though we focus on a proof of the 3d cubic problem, this work presents a new algorithm for verifying certain spectral properties needed to study soliton stability. Source code for verification of our comptuations, and for further experimentation, are available at http://www.math.toronto.edu/simpson/files/spec_prop_code.tgz.Comment: 57 pages, 22 figures, typos fixe

On the uniqueness and global dynamics of AdS spacetimes

We study global aspects of complete, non-singular asymptotically locally AdS spacetimes solving the vacuum Einstein equations whose conformal infinity is an arbitrary globally stationary spacetime. It is proved that any such solution which is asymptotically stationary to the past and future is itself globally stationary. This gives certain rigidity or uniqueness results for exact AdS and related spacetimes.Comment: 18pp, significant revision of v

Uniform energy bound and asymptotics for the Maxwell field on a slowly rotating Kerr black hole exterior

We consider the Maxwell equation in the exterior of a very slowly rotating Kerr black hole. For this system, we prove the boundedness of a positive definite energy on each hypersurface of constant $t$. We also prove the convergence of each solution to a stationary Coulomb solution. We separate a general solution into the charged, Coulomb part and the uncharged part. Convergence to the Coulomb solutions follows from the fact that the uncharged part satisfies a Morawetz estimate, i.e. that a spatially localised energy density is integrable in time. For the unchanged part, we study both the full Maxwell equation and the Fackerell-Ipser equation for one component. To treat the Fackerell-Ipser equation, we use a Fourier transform in $t$. For the Fackerell-Ipser equation, we prove a refined Morawetz estimate that controls 3/2 derivatives with no loss near the orbiting null geodesics.Comment: 50 pages. v3 minor typographical change

Resolvent estimates for normally hyperbolic trapped sets

We give pole free strips and estimates for resolvents of semiclassical operators which, on the level of the classical flow, have normally hyperbolic smooth trapped sets of codimension two in phase space. Such trapped sets are structurally stable and our motivation comes partly from considering the wave equation for Kerr black holes and their perturbations, whose trapped sets have precisely this structure. We give applications including local smoothing effects with epsilon derivative loss for the Schr\"odinger propagator as well as local energy decay results for the wave equation.Comment: Further changes to erratum correcting small problems with Section 3.5 and Lemma 4.1; this now also corrects hypotheses, explicitly requiring trapped set to be symplectic. Erratum follows references in this versio