About general solutions of Euler’s and Navier-Stokes equations

Authors

  • V. I. Rozumniuk Taras Shevchenko National University of Kyiv

DOI:

https://doi.org/10.17721/1812-5409.2019/1.44

Abstract

Constructing a general solution to the Navier-Stokes equation is a fundamental problem of current fluid mechanics and mathematics due to nonlinearity occurring when moving to Euler’s variables. A new transition procedure is proposed without appearing nonlinear terms in the equation, which makes it possible constructing a general solution to the Navier-Stokes equation as a combination of general solutions to Laplace’s and diffusion equations. Existence, uniqueness, and smoothness of the solutions to Euler's and Navier-Stokes equations are found out with investigating solutions to the Laplace and diffusion equations well-studied.

Key words: Euler’s and Navier-Stokes equations, general solutions.

Pages of the article in the issue: 190-193

Language of the article: Ukrainian

References

BATCHELOR, G.K (1973) Vvedenie v dinamiku gidkosti. Moskva: Mir.

KOCHIN, N.E., KIBEL, I.A. and ROZE, N.V. (1963) Teoreticheskaia gidromechanika. v.1,2, Moskva: Fizmatgiz.

SEDOV, L.I. (1970) Mechanika splochnoi sredi. v.1,2, Moskow: Fizmatgiz.

No 1 (2019)

Downloads

How to Cite

Rozumniuk, V. I. (2019). About general solutions of Euler’s and Navier-Stokes equations. Bulletin of Taras Shevchenko National University of Kyiv. Physical and Mathematical Sciences, (1), 190–193. https://doi.org/10.17721/1812-5409.2019/1.44

Issue

No. 1 (2019)

Section

Differential equations, mathematical physics and mechanics

License

Authors who publish with this journal agree to the following terms:

  1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).