Open AccessAbout general solutions of Euler’s and Navier-Stokes equations
Author(s) -
V. I. Rozumniuk
Publication year - 2019
Publication title -
bulletin of taras shevchenko national university of kyiv series physics and mathematics
Language(s) - English
Resource type - Journals
eISSN - 2218-2055
pISSN - 1812-5409
DOI - 10.17721/1812-5409.2019/1.44
Subject(s) - euler equations , mathematics , laplace's equation , uniqueness , smoothness , mathematical analysis , laplace transform , euler's formula , non dimensionalization and scaling of the navier–stokes equations , nonlinear system , navier–stokes equations , semi implicit euler method , backward euler method , hagen–poiseuille flow from the navier–stokes equations , partial differential equation , physics , compressibility , mechanics , quantum mechanics
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.
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