315 citations · 460 across the 13 of their papers we have counts for
13 papers
On the Riemann integrability of the norm of a path in normed spaces
Borys Álvarez-Samaniego, Wilson P. Álvarez-Samaniego, Luis Rivera
A useful result is that if a bounded complex-valued path is Riemann-integrable, then its modulus is also Riemann-integrable. The extension of this last result to bounded paths taki…
On an adjustment to the Fowler equation
Borys Álvarez-Samaniego, Wilson P. Álvarez-Samaniego, Kevin Lloacana-Unda
Following closely the analysis performed by Andrew C. Fowler to derive the first canonical equation for nonlinear dune dynamics, but considering some appropriate changes of variabl…
On the use of the Riesz transforms to determine the pressure term in the incompressible Navier-Stokes equations on the whole space
Borys Álvarez-Samaniego, Wilson P. Álvarez-Samaniego, Pedro G. Fernández-Dalgo
We give some conditions under which the pressure term in the incompressible Navier-Stokes equations on the entire -dimensional Euclidean space is determined by the formula $\dis…
Some properties related to the Cantor-Bendixson derivative on a Polish space
Borys Álvarez-Samaniego, Andrés Merino
We show a necessary and sufficient condition for any ordinal number to be a Polish space. We also prove that for each countable Polish space, there exists a countable ordinal numbe…
Countable ordinal spaces and compact countable subsets of a metric space
Borys Álvarez-Samaniego, Andrés Merino
We show in detail that every compact countable subset of a metric space is homeomorphic to a countable ordinal number, which extends a result given by Mazurkiewicz and Sierpinski f…
Linearized Einstein's field equations
Wilson P. Álvarez-Samaniego, Borys Álvarez-Samaniego, Douglas Moya-Álvarez
From the Einstein field equations, in a weak-field approximation and for speeds small compared to the speed of light in vacuum, the following system is obtained \begin{align*} \nab…
A primitive associated to the Cantor-Bendixson derivative on the real line
Borys Álvarez-Samaniego, Andrés Merino
We consider the class of compact countable subsets of the real numbers . By using an appropriate partition, up to homeomorphism, of this class we give a detailed proof…
Some Existence Results on Cantor Sets
Borys Álvarez-Samaniego, Wilson P. Álvarez-Samaniego, Jonathan Ortiz-Castro
The existence of two different Cantor sets, one of them contained in the set of Liouville numbers and the other one inside the set of Diophantine numbers, is proved. Finally, a nec…
Existence of travelling-wave solutions and local well-posedness of the Fowler equation
Borys Alvarez-Samaniego, Pascal Azerad
We study the existence of travelling-waves and local well-posedness in a subspace of for a nonlinear evolution equation recently proposed by Andrew C. Fowler to…
Comment on "Orbital stability of solitary wave solutions for an interaction equation of short and long dispersive waves"
Borys Alvarez-Samaniego
J. Angulo and J. F. Montenegro (J. Differential Equations 174 (2001), no. 1, 181-199) published a paper about nonlinear stability of solitary waves for an interaction system betwee…
On The Local Well-Posedness for Some Systems of Coupled KdV Equations
Borys Alvarez-Samaniego, Xavier Carvajal
Using the theory developed by Kenig, Ponce, and Vega, we prove that the Hirota-Satsuma system is locally well-posed in Sobolev spaces for…
Large time existence for 3D water-waves and asymptotics
Borys Alvarez-Samaniego, David Lannes
We rigorously justify in 3D the main asymptotic models used in coastal oceanography, including: shallow-water equations, Boussinesq systems, Kadomtsev-Petviashvili (KP) approximati…
A Nash-Moser theorem for singular evolution equations. Application to the Serre and Green-Naghdi equations
Borys Alvarez-Samaniego, David Lannes
We study the well-posedness of the initial value problem for a wide class of singular evolution equations. We prove a general well-posedness theorem under three assumptions easy to…