Existence, blow‐up, and exponential decay estimates for a system of semilinear wave equations associated with the helicalflows of Maxwell fluid. (29th September 2015)

• Record Type: Journal Article
• Authors: Phuong Ngoc, Le Thi; Hoa, Cao Huu; Long, Nguyen Thanh
• Is Part Of: Mathematical methods in the applied sciences. Volume 39:Number 9(2016:Jun. 15)
• Page Start: 2334
• Page End: 2357
• Publication Date: 2015-09-29
• Subjects: system of semilinear wave equations -- mixed nonhomogeneous conditions -- the helical flows of Maxwell fluid -- Faedo–Galerkin method -- blow‐up in finite time -- exponential decay -- subclass 35A01 -- 35A02 -- 35A35 -- 35B40 -- 35B65 -- 35D30; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.3643
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : The paper is devoted to the study of a system of semilinear wave equations associated with the helical flows of Maxwell fluid. First, based on Faedo–Galerkin method and standard arguments of density corresponding to the regularity of initial conditions, we establish two local existence theorems of weak solutions. Next, we prove that any weak solutions with negative initial energy will blow up in finite time. Finally, we give a sufficient condition to guarantee the global existence and exponential decay of weak solutions via the construction of a suitable Lyapunov functional. Copyright © 2015 John Wiley & Sons, Ltd.