# A type D breakdown of the Navier Stokes equation in d=3 spatial dimensions

## TL;DR

This paper demonstrates a specific type D breakdown of the Navier-Stokes equations in three dimensions, highlighting limitations for analytical solutions and emphasizing the need for computational approaches in hydrology applications.

## Contribution

It introduces a novel type D breakdown of the Navier-Stokes equations in three dimensions, extending previous findings and discussing implications for solving hydrology problems.

## Key findings

- Type D breakdown occurs in 3D Navier-Stokes equations.
- Analytical solutions are limited; computational methods are necessary.
- Breakdown also observed in Euler equations.

## Abstract

In this paper a type D breakdown of the Navier Stokes (NS) in d=3 is demonstrated. The element of the breakdown also occurs in the Euler equation. We consider the fact that in d=2 Ladyzhenskaya found a generalized type B solution. The discussion revolves around the notion, also found in quantum spin theory, that in the behavior of a system can be quite different from the behavior in d=2 dimensions. Concerning applications, our resolution of the problem implies that e.g. hydrology problems formulated as a NS equation can only be solved in computational approximation.

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Source: https://tomesphere.com/paper/1703.05113