## Notes on Uniqueness Solutions of Navier-Stokes Equations

**Authors:** Valdir Monteiro dos Santos Godoi

§ 1: remembering the need of imposed the boundary condition u(x,t)=0 at infinity to ensure uniqueness solutions to the Navier-Stokes equations. This section is historical only. § 2: verifying that for potential and incompressible flows there is no uniqueness solutions when the velocity is equal to zero at infinity. More than this, when the velocity is equal to zero at infinity for all t≥0 there is no uniqueness solutions, in general case. Exceptions when u^0=0. § 3: non-uniqueness in time for incompressible and potential flows, if u≠0. § 4: a more general solution of Euler and Navier-Stokes equations for incompressible and irrotational (potential) flows, given the initial velocity. § 5: Solution for Euler and Navier-Stokes equations using Taylor’s series of powers of t around t=0.

**Comments:** 7 Pages.

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### Submission history

[v1] 2016-06-30 08:34:29

[v2] 2016-06-30 18:11:07

[v3] 2016-07-03 20:13:18

[v4] 2016-07-19 14:28:34

[v5] 2016-07-19 18:59:31

[v6] 2016-07-29 20:50:51

[v7] 2016-07-30 08:27:18

[v8] 2016-08-15 15:48:39

[v9] 2016-08-18 14:56:52

[vA] 2016-09-07 12:56:55

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