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

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

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: 190-193Language of the article: Ukrainian