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On a System of Nonlinear Wave Equations Associated with the Helical Flows of Maxwell Fluid: Linear Approximation and Asymptotic Expansion of Solutions in Many Small Parameters

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Abstract

In this paper, a system of nonlinear wave equations associated with the helical flows of Maxwell fluid is studied. Using the Faedo–Galerkin method and the linearization method for nonlinear terms, we prove the existence and uniqueness of a weak solution of the above problem. On the other hand, a new result about asymptotic expansion of high order in many small parameters of a weak solution for the present system is also given.

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Acknowledgments

The authors wish to express their sincere thanks to the referees for the suggestions and valuable comments. The authors are also extremely grateful for the support given by Vietnam’s National Foundation for Science and Technology Development (NAFOSTED) under Project 101.01-2012.12.

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Authors and Affiliations

  1. Nhatrang Educational College, 01 Nguyen Chanh Street, Nhatrang, Khanh Hoa, Vietnam

    Le Thi Phuong Ngoc

  2. Department of Fundamental Sciences, Tra Vinh University, 126, Highway 53, Ward 5, Tra Vinh, Vietnam

    Cao Huu Hoa

  3. Department of Mathematics and Computer Science, University of Natural Science, Vietnam National University Ho Chi Minh City, 227 Nguyen Van Cu Str., Dist. 5, Ho Chi Minh, Vietnam

    Nguyen Thanh Long

Authors
  1. Le Thi Phuong Ngoc
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  2. Cao Huu Hoa
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  3. Nguyen Thanh Long
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Correspondence to Nguyen Thanh Long.

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Phuong Ngoc, L.T., Hoa, C.H. & Long, N.T. On a System of Nonlinear Wave Equations Associated with the Helical Flows of Maxwell Fluid: Linear Approximation and Asymptotic Expansion of Solutions in Many Small Parameters. Vietnam J. Math. 43, 357–384 (2015). https://doi.org/10.1007/s10013-015-0128-0

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  • DOI: https://doi.org/10.1007/s10013-015-0128-0

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