Difficulties with three-dimensional weak solutions for inviscid incompressible flow

Solutions to Three-dimensional Navier-stokes Equations for Incompressible Fluids

This article gives explicit solutions to the space-periodic NavierStokes problem with non-periodic pressure. These type of solutions are not unique and by using such solutions one can construct a periodic, smooth, divergence-free initial vector field allowing a space-periodic and time-bounded external force such that there exists a smooth solution to the 3-dimensional Navier-Stokes equations fo...

Stability of Two-Dimensional Viscous Incompressible Flows under Three-Dimensional Perturbations and Inviscid Symmetry Breaking

In this article we consider weak solutions of the three-dimensional incompressible fluid flow equations with initial data admitting a one-dimensional symmetry group. We examine both the viscous and inviscid cases. For the case of viscous flows, we prove that Leray-Hopf weak solutions of the threedimensional Navier-Stokes equations preserve initially imposed symmetry and that such symmetric flow...

An Optimal Control Formulation for Inviscid Incompressible Ideal Fluid Flow

Research partially supported by the NSF and AFOSR. Work supported in part by NSF and NATO. Work supported by DOE , under contract W-7405-ENG-36. Research partially supported by NSF and AFOSR.

The Solution of Three Dimensional Incompressible Potential Flow Through Rectangular Ducts

The Solution of Three Dimensional Incompressible Potential Flow Through Rectangular Ducts