# The Navier-Stokes Problem

@inproceedings{Ramm2019TheNP, title={The Navier-Stokes Problem}, author={Alexander G. Ramm}, booktitle={Synthesis Lectures on Mathematics and Statistics}, year={2019} }

One of the millennium problems is discussed. The results of the author’s solution to this problem are explained. The problem discussed is the Navier-Stokes problem in the whole space.

## 7 Citations

### Comments on the Navier-Stokes Problem

- Mathematics, PhilosophyAxioms
- 2021

The Navier–Stokes problem (NSP) in R3 without boundaries is proved that the NSP is contradictory in the following sense: if one assumes that the initial data v(x,0)≢0, ∇·v(X,0)=0 and the solution to the N SP exists for all t≥0, then one proves that the solution v (x,t) to theNSP has the property v( x, 0)=0.

### A Closed-Form Analytical Solution to the Complete Three-Dimensional Unsteady Compressible Navier-Stokes Equations

- Physics
- 2021

The three main approaches in fluid dynamics are actual experiments, numerical simulations, and theoretical solutions. Numerical simulations and theoretical solutions are based on the continuity…

### A Closed-Form Analytical Solution to the Complete Three-Dimensional Unsteady Compressible Navier-Stokes Equation

- Physics
- 2021

The three main approaches to exploring fluid dynamics are actual experiments, numerical simulations, and theoretical solutions. Numerical simulations and theoretical solutions are based on the…

### Modeling of the conjugation of vortex flows with downstream in ANSYS

- EngineeringIOP Conference Series: Materials Science and Engineering
- 2019

Using the new technology of longitudinal circulation currents which allows dissipating the excess kinetic energy, thus preventing riverbed erosion and increasing the reliability and environmental…

### Applications of Analytic Continuation to Tables of Integral Transforms and Some Integral Equations with Hyper-Singular Kernels

- MathematicsOpen Journal of Optimization
- 2022

Analytic continuation of some classical formulas with respect to a parameter is discussed. Examples are presented. The validity of these formulas is greatly expanded. Application of these results to…

### When is $F(p)$ the Laplace transform of a bounded $f(t)$?

- Mathematics
- 2022

Sufficient conditions are given for a function F (p), analytic in Rep > 0, to be a Laplace transform of a function f(t), such that maxt≥0|f(t)| < ∞, f(0) = 0.

## References

### Symmetry Problems. The Navier-Stokes Problem

- MathematicsSymmetry Problems. The Navier-Stokes Problem
- 2019

Abstract This book gives a necessary and sufficient condition in terms of the scattering amplitude for a scatterer to be spherically symmetric. By a scatterer we mean a potential or an obstacle. It...