# Low-frequency limit

From DispersiveWiki

The **low-frequency limit** of an equation concerns the behaviour of the equation for solutions which have very low frequency .
This limit is generally only interesting at very large times.
In opposition to the high-frequency limit, it is generally the lower order terms (such as terms associated to mass) which then dominate the behavior. Similarly, regularities which are sub-critical and thus very well behaved in the high-frequency limit, can be very ill-behaved in the low-frequency limit,
although highly nonlinear behavior tends to only manifest itself in the low-frequency limit at very late times.