Geodesic
A new class of non-helical exact solutions of~the~Navier--Stokes equations
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 24 (2020) no. 4, pp. 762-768

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The paper presents a new class of exact solutions for the Navier–Stokes equations. These solutions describe unsteady three-dimensional in velocities and two-dimensional in coordinates for a viscous incompressible fluid flow. The procedure for constructing an exact solution generalizes Trkal's method proposed for studying screw flows. The new class of exact solutions allows to describe non-hecical flows (the velocity vector forms a nonzero angle with the vorticity vector) and fluid flows existing in a finite time.
Keywords: Navier-Stokes equation, Trkal's method, eigenfunctions of the Laplacian, non-helical flows, blow-up regimes.
Mots-clés : exact solution 
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     author = {V. P. Kovalev and E. Yu. Prosviryakov},
     title = {A new class of non-helical exact solutions {of~the~Navier--Stokes}  equations},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {762--768},
     publisher = {mathdoc},
     volume = {24},
     number = {4},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2020_24_4_a8/}
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V. P. Kovalev; E. Yu. Prosviryakov. A new class of non-helical exact solutions of~the~Navier--Stokes  equations. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 24 (2020) no. 4, pp. 762-768. http://geodesic.mathdoc.fr/item/VSGTU_2020_24_4_a8/