Two-dimensional cavity flow in an infinitely long channel with non-zero vorticity
The well-posedness theory of the incompressible inviscid cavity flow in an infinitely long channel is investigated. The flow is governed by a two-dimensional incompressible steady system. By establishing the existence and uniqueness of the incompressible cavity flow in an infinitely long symmetric channel, which contains a smooth free surface detaching at a boundary point of the obstacle, and then pointing out the asymptotic behavior of the cavity flow together with the positivity of the horizontal velocity, the authors finally show that there does not exist a finite cavity or a cusped cavity in an infinitely long nozzle, which gives a positive answer to the \textit{H. Villat} conjecture [Ann. Fac. Sci. Toulouse Sci. Math. Sci. Phys., 3 (5), 375--404 (1913; \url{doi:10.5802/afst.292})] on the non-existence of a finite cusped cavity behind an obstacle.
scientific article; zbMATH DE number 6756310
scientific article