Arkadiy Tsionskiy, Mikhail Tsionskiy
Abstract:
Solutions of the Navier-Stokes and Euler equations with initial conditions
for 2D and 3D cases were obtained in the form of converging series, by
an analytical iterative method using Fourier and Laplace transforms in [28,29].
There the solutions are infinitely differentiable functions, and for
several combinations of parameters numerical results are presented.
This article provides a detailed proof of the existence, uniqueness and
smoothness of the solution of the Cauchy problem for the 3D Navier-Stokes
equations with any smooth initial velocity. When the viscosity tends to
zero, this proof applies also to the Euler equations.
Submitted December 10, 2012. Published April 5, 2013.
Math Subject Classifications: 35Q30, 76D05.
Key Words: 3D Navier-Stokes equations; Fourier transform;
Laplace transform; fixed point principle.
An addendum as posted on December 31, 2013. It indicates that some results are incorrect. See the last page of this article.
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Arkadiy Tsionskiy Department of Civil Environmental and Ocean Engineering Stevens Institute of Technology Hoboken, NJ 07030, USA email: amtsionsk@gmail.com |
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Mikhail Tsionskiy Department of Civil Environmental and Ocean Engineering Stevens Institute of Technology Hoboken, NJ 07030, USA email: amtsionsk@gmail.com |
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