• On the influence of gravity on density-dependent incompressible periodic fluids 

  Ngo V.-S.; Scrobogna S. (J. Differential Equations, 2019)

  The present work is devoted to the analysis of density-dependent, incompressible fluids in a 3D torus, when the Froude number $\varepsilon$ goes to zero. We consider the very general case where the initial data do not have ...

• Unique determination of the electric potential in the presence of a fixed magnetic potential in the plane 

  Caro P.; Rogers K. (2018-12)

  For electric and magnetic potentials with compact support, we consider the magnetic Schrödinger equation with fixed positive energy. Under a mild additional regularity hypothesis, and with fixed magnetic potential, we show ...

• Determination of convection terms and quasi-linearities appearing in diffusion equations 

  Caro P.; Kian Y. (2018-12)

  We consider the highly nonlinear and ill posed inverse problem of determining some general expression appearing in the a diffusion equation from measurements of solutions on the lateral boundary. We consider both linear ...

• Correlation imaging in inverse scattering is tomography on probability distributions 

  Caro P.; Helin T.; Kujanpää A.; Lassas M. (Inverse Problems, 2018-12-04)

  Scattering from a non-smooth random field on the time domain is studied for plane waves that propagate simultaneously through the potential in variable angles. We first derive sufficient conditions for stochastic moments ...

• Two-weight mixed norm estimates for a generalized spherical mean Radon transform acting on radial functions 

  Ciaurri Ó.; Nowak, A.; Roncal, L. (SIAM Journal on Mathematical Analysis, 2018)

  We investigate a generalized spherical means operator, viz. generalized spherical mean Radon transform, acting on radial functions. We establish an integral representation of this operator and find precise estimates of ...

• Vector-valued extensions for fractional integrals of Laguerre expansions 

  Ciaurri Ó.; Roncal L. (Studia Math., 2018)

  We prove some vector-valued inequalities for fractional integrals defined for several orthonormal systems of Laguerre functions. On the one hand, we obtain weighted $L^p-L^q$ vector-valued extensions, in a multidimensional ...

• Hölder-Lebesgue regularity and almost periodicity for semidiscrete equations with a fractional Laplacian 

  Lizama C.; Roncal L. (Discrete Contin. Dyn. Syst., 2018)

  We study the equations $ \partial_t u(t,n) = L u(t,n) + f(u(t,n),n); \partial_t u(t,n) = iL u(t,n) + f(u(t,n),n)$ and $ \partial_{tt} u(t,n) =Lu(t,n) + f(u(t,n),n)$, where $n\in \mathbb{Z}$, $t\in (0,\infty)$, and $L$ ...

• Nonlocal discrete diffusion equations and the fractional discrete Laplacian, regularity and applications 

  Ciaurri Ó.; Roncal L.; Stinga P.R.; Torrea J.L.; Varona J.L. (Adv. Math., 2018)

  The analysis of nonlocal discrete equations driven by fractional powers of the discrete Laplacian on a mesh of size $h>0$ \[ (-\Delta_h)^su=f, \] for $u,f:\Z_h\to\R$, $0<s<1$, is performed. The pointwise nonlocal ...

• Hardy-type inequalities for fractional powers of the Dunkl-Hermite operator 

  Ciaurri Ó.; Roncal L.; Thangavelu S. (Proc. Edinburgh Math. Soc. (2), 2018)

  We prove Hardy-type inequalities for a fractional Dunkl–Hermite operator, which incidentally gives Hardy inequalities for the fractional harmonic oscillator as well. The idea is to use h-harmonic expansions to reduce the ...

• A Global well-posedness result for the Rosensweig system of ferrofluids 

  Scrobogna S.; De Anna F. (Rev. Mat. Iberoam., 2019)

  In this Paper we study a Bloch-Torrey regularization of the Rosensweig system for ferrofluids. The scope of this paper is twofold. First of all, we investigate the existence and uniqueness of Leray-Hopf solutions of this ...

• Vector-valued operators, optimal weighted estimates and the $C_p$ condition 

  Cejas M.E.; Li K.; Pérez C.; Rivera-Ríos I.P. (Science China Mathematics, 2018-09)

  In this paper some new results concerning the $C_p$ classes introduced by Muckenhoupt and later extended by Sawyer, are provided. In particular we extend the result to the full range expected $p>0$, to the weak norm, to ...

• Asymptotic behaviour of neuron population models structured by elapsed-time 

  Cañizo J.A.; Yoldas H. (Nonlinearity, 2019-01-04)

  We study two population models describing the dynamics of interacting neurons, initially proposed by Pakdaman et al (2010 Nonlinearity 23 55–75) and Pakdaman et al (2014 J. Math. Neurosci. 4 1–26). In the first model, the ...

• El efecto de Talbot: de la óptica a la ecuación de Schrödinger 

  Eceizabarrena D. (TEMat, 2017-07)

  El objetivo de este artículo es dar a conocer un bello efecto óptico que se denomina efecto de Talbot. Primero, describiremos el fenómeno y comentaremos su descubrimiento a mediados del siglo XIX. A continuación, analizaremos ...

• Robust numerical methods for nonlocal (and local) equations of porous medium type. Part II: Schemes and experiments 

  del Teso F.; Endal J.; Jakobsen E.R. (SIAM Journal on Numerical Analysis, 2018)

  \noindent We develop a unified and easy to use framework to study robust fully discrete numerical methods for nonlinear degenerate diffusion equations $$ \partial_t u-\mathfrak{L}[\varphi(u)]=f(x,t) \qquad\text{in}\qquad ...

• Uniqueness of degree-one Ginzburg–Landau vortex in the unit ball in dimensions N ≥ 7 

  Ignat R.; Nguyen L.; Slastikov V.; Zarnescu A. (Comptes Rendus Mathematique, 2018-09-01)

  For ε>0, we consider the Ginzburg-Landau functional for RN-valued maps defined in the unit ball BN⊂RN with the vortex boundary data x on ∂BN. In dimensions N≥7, we prove that for every ε>0, there exists a unique global ...

• Shear flow dynamics in the Beris-Edwards model of nematic liquid crystals 

  Murza A.C.; Teruel A.E.; Zarnescu A. (Proceedings of the Royal Society A-Mathematical, Physical and Engineering Sciences, 2018-02-14)

  We consider the Beris-Edwards model describing nematic liquid crystal dynamics and restrict to a shear flow and spatially homogeneous situation. We analyze the dynamics focusing on the effect of the flow. We show that in ...

• Dynamics and flow effects in the Beris-Edwards system modeling nematic liquid crystals 

  Hao W; Xiang X; Zarnescu A (Archive for Rational Mechanics and Analysis, 2018-08-10)

  We consider the Beris-Edwards system modelling incompressible liquid crystal flows of nematic type. This couples a Navier-Stokes system for the fluid velocity with a parabolic reaction-convection-diffusion equation for the ...

• Some remark on the existence of infinitely many nonphysical solutions to the incompressible Navier-Stokes equations 

  Scrobogna S. (Journal of Mathematical Analysis and Applications, 2018-10)

  We prove that there exist infinitely many distributional solutions with infinite kinetic energy to both the incompressible Navier-Stokes equations in $ \mathbb{R}^2 $ and Burgers equation in $\mathbb{R} $ with vanishing ...

• Proof of an extension of E. Sawyer's conjecture about weighted mixed weak-type estimates 

  Li K.; Ombrosi S.; Pérez C. (Mathematische Annalen, 2018-09)

  We show that if $v\in A_\infty$ and $u\in A_1$, then there is a constant $c$ depending on the $A_1$ constant of $u$ and the $A_{\infty}$ constant of $v$ such that $$\Big\|\frac{ T(fv)} {v}\Big\|_{L^{1,\infty}(uv)}\le c\, ...

• On the global well-posedness of a class of 2D solutions for the Rosensweig system of ferrofluids 

  Scrobogna S. (Journal of Differential Equations, 2018-09)

  We study a class of 2D solutions of a Bloch-Torrey regularization of the Rosensweig system in the whole space, which arise when the initial data and the external magnetic field are 2D. We prove that such solutions are ...

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