20 citations · 25 across the 11 of their papers we have counts for
13 papers
On a Generalized System with Applications to Ideal Magnetohydrodynamics
Alejandro Sarria
Finite-time blowup of solutions to a generalized system of equations with applications to ideal Magnetohydrodynamics (MHD) and one-dimensional fluid convection an…
Blowup of Solutions to a Damped Euler Equation with Homogeneous Three-Point Boundary Condition
Ikechukwu Obi-Okoye, Alejandro Sarria
It has been established that solutions to the inviscid Proudman-Johnson equation subject to a homogeneous three-point boundary condition can develop singularities in finite time. I…
On the regularity of solutions to the generalized Hunter-Saxton system
Jaeho Choi, Nitin Krishna, Nicole Magill +1
The generalized Hunter-Saxton system comprises several well-known models from fluid dynamics and serves as a tool for the study of fluid convection and stretching in one-dimensiona…
Damped Infinite Energy Solutions of the 3D Euler and Boussinesq Equations
William Chen, Alejandro Sarria
We revisit a family of infinite-energy solutions of the 3D incompressible Euler equations proposed by Gibbon et al. [9] and shown to blowup in finite time by Constantin [6]. By add…
Lagrangian aspects of the axisymmetric Euler equation
Stephen C. Preston, Alejandro Sarria
In this paper we are interested in geometric aspects of blowup in the axisymmetric 3D Euler equations with swirl on a cylinder. Writing the equations in Lagrangian form for the flo…
A sign-changing Liouville Equation
Alejandro Sarria, Ralph Saxton
We examine periodic solutions to an initial boundary value problem for a Liouville equation with sign-changing weight. A representation formula is derived both for singular and non…
Blowup in Stagnation-point Form Solutions of the Inviscid 2d Boussinesq Equations
Alejandro Sarria, Jiahong Wu
The 2d Boussinesq equations model large scale atmospheric and oceanic flows. Whether its solutions develop a singularity in finite-time remains a classical open problem in mathemat…
One-parameter solutions of the Euler-Arnold equation on the contactomorphism group
Stephen C. Preston, Alejandro Sarria
We study solutions of the equation which arises by considering solutions of the Euler-Arnold equa…
Global estimates and blow-up criteria for the generalized Hunter-Saxton system
Alejandro Sarria
The generalized, two-component Hunter-Saxton system comprises several well-known models of fluid dynamics and serves as a tool for the study of one-dimensional fluid convection and…
Critical Buckling Loads of the Perfect Hollomon's Power-law Columns
Dongming Wei, Alejandro Sarria, Mohamed Elgindi
In this work, we present analytic formulas for calculating the critical buckling states of some plastic axial columns of constant cross-sections. The associated critical buckling l…
The Role of Initial Curvature in Solutions to the Generalized Inviscid Proudman-Johnson Equation
Alejandro Sarria, Ralph Saxton
In [20], we derived representation formulae for spatially periodic solutions to the generalized, inviscid Proudman-Johnson equation and studied their regularity for several classes…
Blow-up of Solutions to the Generalized Inviscid Proudman-Johnson Equation
Alejandro Sarria, Ralph Saxton
For arbitrary values of a parameter , finite-time blow-up of solutions to the generalized, inviscid Proudman-Johnson equation is studied via a direct approach which involve…
Regularity of Stagnation Point-form Solutions of the Two-dimensional Euler Equations
Alejandro Sarria
A class of semi-bounded solutions of the two-dimensional incompressible Euler equations satisfying either periodic or Dirichlet boundary conditions is examined. For smooth initial…