why you warry about the analytical solutions of Navier-Stokes equations and the simplest analytical solution was introduced recently with some applications of fluid flow in 2D and 3 since 2022 and 2023 by Mohammadein S A et al
Just you write
Simplest and analytical solutions of Navier-Stokes equations
The transformation of Non linear to linear Navier-Stokes equations and analytical solutions to linear Navier-Stokes equations with application are obtained in this published paper:
The Simplest Analytical Solution of Navier-Stokes Equations
Mohammadein S. A., R. A. Gad El-Rab and Maha S. Ali
Inf. Sci. Lett. 10, No. 2, 159-165 (2021)
In the Lagrange formulation, the Navier-Stokes equations for an incompressible fluid are linear (see appendix).
Therefore, they may well have an analytical solution.
F. D. Sorokin
what kind of equation is? A second time derivative of velocity shouldn’t be the lagrangian derivative ? Furthermore, the lack of the diffusive term means you work with Euler equations.
Dr. F. Sorokin your equation is wave equation and not Navier-stokes equation
But mass and Navier-Stokes equations are as follows:
Mass equation
∇.v=0,
Navier-Stokes equation
1.In Lagrange description [Fluid assumed as a particle]
𝑑v𝑑𝑡=−1/𝜌∇𝑃+𝜈∇*2 v
Or in Euler description [Fluid assumed as a point]
2. 𝜕v𝜕𝑡+(v.∇)v=−1/𝜌 ∇𝑃+𝜈∇*2 v
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