## Bounds on the growth of the support of a vortex path.(English)Zbl 0839.76010

Summary: We study the time evolution of the support of a vortex patch evolving in $$\mathbb{R}^2$$ according to the Euler equation for an incompressible fluid and we bound its growth. Furthermore, we discuss the same problem in the framework of a simplified model. Finally, we consider a similar problem for the Navier-Stokes flow.

### MSC:

 76B47 Vortex flows for incompressible inviscid fluids 35Q35 PDEs in connection with fluid mechanics 35Q30 Navier-Stokes equations

### Keywords:

time evolution; Euler equation
Full Text:

### References:

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