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Volume 9, Issue 2
Weakly Nonlinear Oscillatory Waves with Multi-phases in Ideal Incompressible Fluid

Ming Chen & Qingjiu Qiu

J. Part. Diff. Eq., 9 (1996), pp. 139-152.

Published online: 1996-09

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  • Abstract
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.
  • Keywords

Weakly nonlinear geometric optics ideal incompressible fluids oscillatory waves with multi-phases

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COPYRIGHT: © Global Science Press

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@Article{JPDE-9-139, author = {Ming Chen and Qingjiu Qiu }, title = {Weakly Nonlinear Oscillatory Waves with Multi-phases in Ideal Incompressible Fluid}, journal = {Journal of Partial Differential Equations}, year = {1996}, volume = {9}, number = {2}, pages = {139--152}, abstract = { 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.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5616.html} }
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.
Ming Chen and Qingjiu Qiu . (1996). Weakly Nonlinear Oscillatory Waves with Multi-phases in Ideal Incompressible Fluid. Journal of Partial Differential Equations. 9 (2). 139-152. doi:
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