Blowup of Solutions to a Damped Euler Equation with Homogeneous Three-Point Boundary Condition

Authors

  • Ikechukwu Obi-Okoye Georgia Institute of Technology
  • Alejandro Sarria University of North Georgia

DOI:

https://doi.org/10.46787/pump.v5i0.2882

Keywords:

generalized Proudman-Johnson equation; blowup; three-point boundary condition; damping

Abstract

It is known that solutions to the inviscid Proudman-Johnson equation subject to a homogeneous three-point boundary condition can develop singularities in finite time. Given the regularizing effect that damping can have, in this paper we consider the possibility of finite-time singularity formation in solutions of the generalized inviscid Proudman-Johnson equation with damping subject to the same homogeneous three-point boundary condition. In particular, we will derive criteria the initial condition must satisfy in order for solutions to blowup in finite time under the effect of a smooth time-dependent damping term.   

Author Biography

Alejandro Sarria, University of North Georgia

Associate Professor, Department of Mathematics.

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Published

2022-06-18

How to Cite

Obi-Okoye, I. ., & Sarria, A. (2022). Blowup of Solutions to a Damped Euler Equation with Homogeneous Three-Point Boundary Condition. The PUMP Journal of Undergraduate Research, 5, 152–160. https://doi.org/10.46787/pump.v5i0.2882