Susana Gutiérrez
University of Birmingham
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Publication
Featured researches published by Susana Gutiérrez.
Pediatric Dermatology | 2003
Susana Gutiérrez; Judith Rivas; Luis Vega
Abstract The dynamical behavior of an isolated vortex filament in three dimensions within the localized induction approximation (LIA) is investigated. It is shown the existence of a uniparametric family of smooth solutions of LIA that generates a corner in finite time. An explicit formula of the solution is provided in terms of the curvature of the initial regular configuration. The behavior of the uniparametric family of solutions with respect to the free parameter is also considered. †Dedicated to the memory of Björn E. J. Dahlberg.
Communications in Partial Differential Equations | 2008
Nikolaos Bournaveas; Vincent Calvez; Susana Gutiérrez; Benoît Perthame
We investigate further the existence of solutions to kinetic models of chemotaxis. These are nonlinear transport-scattering equations with a quadratic nonlinearity which have been used to describe the motion of bacteria since the 80s when experimental observations have shown they move by a series of ‘run and tumble’. The existence of solutions has been obtained in several papers Chalub et al. (2004), Hwang et al. (2005a b) using direct and strong dispersive effects. Here, we use the weak dispersion estimates of Castella and Perthame (1996) to prove global existence in various situations depending on the turning kernel. In the most difficult cases, where both the velocities before and after tumbling appear, with the known methods, only Strichartz estimates can give a result, with a smallness assumption.
Nonlinearity | 2004
Susana Gutiérrez; Luis Vega
We investigate the formation of singularities in a self-similar form of regular solutions of the localized induction approximation (also referred as to the binormal flow). This equation appears as an approximation model for the self-induced motion of a vortex filament in an inviscid incompressible fluid. The solutions behave as 3D-logarithmic spirals at infinity.The proofs of the results are strongly based on the existing connection between the binormal flow and certain Schrodinger equations.
Proceedings of the American Mathematical Society | 2000
Susana Gutiérrez
It is shown that the Bochner-Riesz operator on Rn of negative order α is of restricted weak type in the critical points (p0, q0) and (q′ 0, p′0), where 1/q0 = 3/4 + α/2, q0 = p′0/3 for −3/2 < α < 0 in the two-dimensional case and 1/q0 = (n + 1 + 2α)/2n, q0 = (n − 1)p′0/(n + 1), for −(n + 1)/2 < α < −1/2 if n ≥ 3.
Communications in Partial Differential Equations | 2014
Jonathan Bennett; Neal Bez; Susana Gutiérrez; Sanghyuk Lee
We show that the endpoint Strichartz estimate for the kinetic transport equation is false in all dimensions. We also present an alternative approach to proving the non-endpoint cases using multilinear analysis.
Revista Matematica Iberoamericana | 2007
Nikolaos Bournaveas; Susana Gutiérrez
We study the smoothing effect of averaging over spheres for solutions of kinetic transport equations in hyperbolic Sobolev spaces.
Revista Matematica Iberoamericana | 2013
Jonathan Bennett; Neal Bez; Susana Gutiérrez
Abstract. We prove local “L-improving” estimates for a class of multilinear Radon-like transforms satisfying a strong transversality hypothesis. As a consequence, we obtain sharp multilinear convolution estimates for measures supported on fully transversal submanifolds of Euclidean space of arbitrary dimension. Motivated by potential applications in diffraction tomography, we also prove global estimates for the same class of Radon-like transforms under a natural homogeneity assumption.
Siam Journal on Mathematical Analysis | 2008
Nikolaos Bournaveas; Susana Gutiérrez
We prove estimates in hyperbolic Sobolev spaces
Nonlinearity | 2015
Susana Gutiérrez; André de Laire
H^{s,\delta}(R^{1+d})
Mathematische Annalen | 2004
Susana Gutiérrez
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