One method for constructing exact solutions of equations of two-dimensional hydrodynamics of an incompressible fluid

TL;DR

This paper introduces an algebraic method to construct exact solutions for the equations governing two-dimensional incompressible fluid hydrodynamics, simplifying the process for both viscous and nonviscous cases.

Contribution

It presents a novel algebraic approach that reduces the problem to solving linear PDEs and ODEs, streamlining solution construction for fluid dynamics equations.

Findings

Method simplifies solution process for 2D hydrodynamics equations

Applicable to both viscous and nonviscous fluids

Facilitates exact solutions construction

Abstract

We propose a simple algebraic method for constructing exact solutions of equations of two-dimensional hydrodynamics of an incompressible fluid. The problem reduces to consecutively solving three linear partial differential equations for a nonviscous fluid and to solving three linear partial differential equations and one first-order ordinary differential equation for a viscous fluid.