Rough dependence upon initial data exemplified by explicit solutions and the effect of viscosity

TL;DR

This paper presents explicit solutions demonstrating rough dependence on initial data and explores viscous effects, extending Cauchy's theorem to viscous cases, highlighting the sensitivity of solutions to initial conditions and viscosity.

Contribution

It introduces explicit solutions illustrating rough dependence and extends Cauchy's theorem to viscous flows, advancing understanding of initial data sensitivity.

Findings

Explicit solutions showing rough dependence on initial data

Extension of Cauchy's theorem to viscous cases

Analysis of viscous effects on solution behavior

Abstract

In this article, we present some explicit solutions showing rough dependence upon initial data. We also studies viscous effects. An extension of a theorem of Cauchy to the viscous case is also presented.