Compensated compactness

From DispersiveWiki


Compensated compactness is the principle that certain bilinear or nonlinear operators may exhibit some unexpectedly good compactness properties (e.g. map bounded sequences to precompact sequences in a suitable strong topology) if they exhibit some cancellation in their internal structure. It is of particular importance in conservation law equations. For nonlinear dispersive and wave equations, the counterpart of this principle appears to be the null form estimates. See also concentration compactness, which is another way of salvaging a type of compactness from a non-compact situation.