A Riccatitype solution of 3D Euler equations for incompressible flow
Abstract
In fluid mechanics, a lot of authors have been reporting analytical solutions of Euler and NavierStokes equations. But there is an essential deficiency of nonstationary solutions indeed. In our presentation, we explore the case of nonstationary flows of the Euler equations for incompressible fluids, which should conserve the Bernoullifunction to be invariant for the aforementioned system. We use previously suggested ansatz for solving of the system of NavierStokes equations (which is proved to have the analytical way to present its solution in case of conserving the Bernoullifunction to be invariant for such the type of the flows). Conditions for the existence of exact solution of the aforementioned type for the Euler equations are obtained. The restrictions at choosing of the form of the 3D nonstationary solution for the given constant Bernoullifunction B are considered. We should especially note that pressure field should be calculated from the given constant Bernoullifunction B, if all the components of velocity field are obtained.
 Publication:

arXiv eprints
 Pub Date:
 March 2018
 arXiv:
 arXiv:1804.00543
 Bibcode:
 2018arXiv180400543E
 Keywords:

 Physics  Fluid Dynamics;
 35Q35
 EPrint:
 18 pages, 3 figures