TY - JOUR
T1 - Dispersion Estimates for Third Order Equations in Two Dimensions
AU - Ben-Artzi, Matania
AU - Koch, Herbert
AU - Saut, Jean Claude
PY - 2003
Y1 - 2003
N2 - Two-dimensional deep water waves and some problems in nonlinear optics can be described by various third order dispersive equations, modifying and generalizing the KdV as well as nonlinear Schrödinger equations. We classify all third order polynomials up to certain transformations and study the pointwise decay for the fundamental solutions, ∫ℝ2e itp(ξ)+ix·ξ dξ for all third order polynomials p in two variables. We deduce the corresponding Strichartz estimates. These estimates imply global existence and uniqueness for the Shrira system.
AB - Two-dimensional deep water waves and some problems in nonlinear optics can be described by various third order dispersive equations, modifying and generalizing the KdV as well as nonlinear Schrödinger equations. We classify all third order polynomials up to certain transformations and study the pointwise decay for the fundamental solutions, ∫ℝ2e itp(ξ)+ix·ξ dξ for all third order polynomials p in two variables. We deduce the corresponding Strichartz estimates. These estimates imply global existence and uniqueness for the Shrira system.
KW - Dispersive equations
KW - Oscillatory integrals
KW - Shrira system
KW - Third-order phase function
UR - https://www.scopus.com/pages/publications/0345358547
U2 - 10.1081/PDE-120025491
DO - 10.1081/PDE-120025491
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AN - SCOPUS:0345358547
SN - 0360-5302
VL - 28
SP - 1943
EP - 1974
JO - Communications in Partial Differential Equations
JF - Communications in Partial Differential Equations
IS - 11-12
ER -