Darboux transformations for two classes of incompressible fluid equations (Q2925032)

From the predecessors results it follows that Darboux transformations play key roles in the investigation of finite time blow-up solutions to 2D quasi-geostrophic equations and 2D or 3D incompressible inviscid Euler equations. Also the Darboux transformations were utilized to study the global well-posedness of 3D Navier-Stokes equations.NEWLINENEWLINENEWLINEIn the reviewed article the authors give new and general Darboux transformations for 2D quasigeostrophic equation arising at the description of the transportation of the potential temperature \(\theta\) by an incompressible flow and 3D incompressible inviscid Euler equations in vorticity form. The obtained results show the good correspondence in the applications of the Darboux transformation for both these equations.