Singularity formation in the contour dynamics for 2d Euler equation on the plane

Abstract: We will study 2d Euler dynamics of centrally symmetric pair of patches on the plane. In the presence of exterior regular velocity, we will show that these patches can merge so fast that the distance between them allows double-exponential upper bound which is known to be sharp. The formation of the 90 degree corners on the interface and the self-similarity analysis of this process will be discussed. For a model equation, we will discuss existence of the curve of smooth stationary solutions that originates at singular stationary steady state.

mathematical physicsanalysis of PDEsdynamical systems

Audience: researchers in the topic

Dynamical systems and PDEs

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