Abstract
We investigate the decay for of weak Sobolev-type solutions of semilinear nonlocal equations . We consider the case when is an elliptic Fourier multiplier with polyhomogeneous symbol , and we derive algebraic decay estimates in terms of weighted Sobolev norms. Our basic example is the celebrated Benjamin–Ono equation
for internal solitary waves of deep stratified fluids. Their profile presents algebraic decay, in strong contrast with the exponential decay for KdV shallow water waves.
Citation
Marco Cappiello. Todor Gramchev. Luigi Rodino. "Decay estimates for solutions of nonlocal semilinear equations." Nagoya Math. J. 218 175 - 198, June 2015. https://doi.org/10.1215/00277630-2891745
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