Wild solutions for 2D incompressible ideal flow with passive tracer

Comparison of three different numerical schemes for 2D steady incompressible lid-driven cavity flow

In this study, a numerical solution of 2D steady incompressible lid-driven cavity flow is presented. Three different numerical schemes were employed to make a comparison on the practicality of the methods. An alternating direction implicit scheme for the vorticity-stream function formulation, explicit and implicit schemes for the primitive variable formulation of governing Navier-Stokes equatio...

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.

Uniqueness for Two-Dimensional Incompressible Ideal Flow on Singular Domains

We prove uniqueness of the weak solution of the Euler equations for compactly supported, single signed and bounded initial vorticity in simply connected planar domains with corners forming angles larger than π/2. In this type of domain, the velocity is not log-lipschitz and does not belong to W 1,p for all p, which is the standard regularity for the Yudovich’s arguments. Thanks to the explicit ...

An incompressible 2D didactic model with singularity and explicit solutions of the 2D Boussinesq equations

We give an example of a well posed, finite energy, 2D incompressible active scalar equation with the same scaling as the surface quasi-geostrophic equation and prove that it can produce finite time singularities. In spite of its simplicity, this seems to be the first such example. Further, we construct explicit solutions of the 2D Boussinesq equations whose gradients grow exponentially in time ...

Two Dimensional Incompressible Ideal Flow Around a Small Curve