Dispersive Estimates for Linearized Water Wave-Type Equations in Rd
Deneke T. Dufera T.T. Tesfahun A.
November 2023Birkhauser
Annales Henri Poincare
2023#24Issue 113741 - 3761 pp.
We derive a Lx1(Rd)-Lx∞(Rd) decay estimate of order O(t-d/2) for the linear propagators exp(±it|D|(1+β|D|2)tanh|D|),β∈{0,1}.D=-i∇, with a loss of 3d/4 or d/4–derivatives in the case β= 0 or β= 1 , respectively. These linear propagators are known to be associated with the linearized water wave equations, where the parameter β measures surface tension effects. As an application, we prove low regularity well-posedness for a Whitham–Boussinesq-type system in Rd , d≥ 2 . This generalizes a recent result by Dinvay, Selberg and the third author where they proved low regularity well-posedness in R and R2 .
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Department of Mathematics, Nazarbayev University, Qabanbai Batyr Avenue 53, Nur-Sultan, 010000, Kazakhstan
Department of Mathematics, Adama University of Science and Technology, Adama, Ethiopia
Department of Mathematics
Department of Mathematics
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