TY - JOUR
T1 - Weakly Nonlinear Oscillatory Waves with Multi-phases in Ideal Incompressible Fluid
AU - Ming Chen  & Qingjiu Qiu 
JO - Journal of Partial Differential Equations
VL - 2
SP - 139
EP - 152
PY - 1996
DA - 1996/09
SN - 9
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5616.html
KW - Weakly nonlinear geometric optics
KW - ideal incompressible fluids
KW - oscillatory waves with multi-phases
AB -  In this paper, we apply the technique of weakly nonlinear geometric optics to study weakly nonlinear oscillatory waves with multi-phases in d-dimensional ideal incompressible fluid for d ≥ 2. Precisely, we give a rigorous asymptotic expansion for the solution of the oscillatory initial value problem to the ideal incompressible Euler equations. Generally, this problem is not well posed. However, the coherence assumption and small divisor property imposed on the phases functions lead to a compatibility condition for the solvability of profile equations from which we can determine every profile.