Cauchy problem for a higher order generalized Boussinesq-type equation with hydrodynamical damped term. Issue 3 (3rd March 2016)

• Record Type: Journal Article
• Authors: Di, Huafei; Shang, Yadong
• Is Part Of: Applicable analysis. Volume 95:Issue 3(2016)
• Page Start: 690
• Page End: 714
• Publication Date: 2016-03-03
• Subjects: Boussinesq-type equation -- Cauchy problem -- higher order -- existence of solutions -- blow up -- hydrodynamical damped term; 35L30 -- 35L82 -- 35D40 -- 35B44; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2015.1026811
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : We consider the existence and nonexistence of global weak solutions to the Cauchy problem for a higher order generalized Boussinesq-type equation with hydrodynamical damped term in -dimensional space. The existence of global weak solutions is proved under the assumptions that the nonlinear term is polynomial growth order, either, , the constant, or the initial data belongs to the potential well. Moreover, we establish two finite-time blow up results for any weak solutions with negative initial energy or nonnegative initial energy using the concavity method.