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Singular integral system approach to regularity of 3D vortex patches. (English) Zbl 0993.35077

The three-dimensional incompressible Euler system with discontinuous initial data is studied. The author shows that this problem is equivalent to some singular integral system with respect to the fluid path. Existence and regularity of solutions of the singular integral system are established in general setting. The regularity of uniform Hölder type for the vorticity \(\omega (x,t)\) is established for a short time. The global regularity of \(\omega \) for axisymmetric flows is established.

MSC:

35Q35 PDEs in connection with fluid mechanics
31B10 Integral representations, integral operators, integral equations methods in higher dimensions
76B47 Vortex flows for incompressible inviscid fluids
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