## Abstract / Description of output

For a periodic vector field F, let

Xϵ solve the dynamical system

dXϵdt=F(Xϵϵ).

In \cite{DeGiorgi} Ennio De Giorgi enquiers whether from the existence of the limit X0(t):=limϵ→0Xϵ(t) one can conclude that dX0dt=constant. Our main result settles this conjecture under fairly general assumptions on F, which may also depend on t-variable.

Once the above problem is solved, one can apply the result to the transport equation, in a standard way. This is also touched upon in the text to follow.

Xϵ solve the dynamical system

dXϵdt=F(Xϵϵ).

In \cite{DeGiorgi} Ennio De Giorgi enquiers whether from the existence of the limit X0(t):=limϵ→0Xϵ(t) one can conclude that dX0dt=constant. Our main result settles this conjecture under fairly general assumptions on F, which may also depend on t-variable.

Once the above problem is solved, one can apply the result to the transport equation, in a standard way. This is also touched upon in the text to follow.

Original language | English |
---|---|

Publisher | ArXiv |

Number of pages | 15 |

Publication status | Published - 29 Dec 2015 |