Low-frequency limit

The low-frequency limit of an equation concerns the behaviour of the equation for solutions which have very low frequency $|\xi |\to 0$. 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.