## 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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### References:

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