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Transport equations due to the non-Lipschitzian vector fields and fluid mechanics. (Equations de transport relatives à des champs de vecteurs non- lipschitziens et mécanique des fluides.) (French) Zbl 0821.76012
The authors study the properties of transport equations due to logarithmic Lipschitzian vector fields, i.e. equations of the type \(\partial_ tf + \text{div} (fv) = g\), \(f |_{t=0} = f_ 0\). They prove the existence of a unique solution in certain function spaces and show that such vector fields possess a flow whose Hölder regularity is exponentially decreasing.

MSC:
76B47 Vortex flows for incompressible inviscid fluids
35Q35 PDEs in connection with fluid mechanics
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