Global existence of solutions for hyperbolic Navier–Stokes equations in three space dimensions

Article type: Research Article

Authors: Abdelhedi, Bouthaina^{; *}

Affiliations: Department of Mathematics, Faculty of Sciences of Sfax, University of Sfax, BP1171, Sfax 3000, Tunisia. E-mail: [email protected]

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: We consider a hyperbolic quasilinear perturbation of the Navier–Stokes equations in three space dimensions. We prove global existence and uniqueness of solutions for initial data and forcing terms, which are larger and less regular than in previous works. Furthermore, we prove the convergence of solutions to relaxed system towards solutions to the classical Navier–Stokes problem.

Keywords: Hyperbolic Navier–Stokes equations, global existence, quasilinear hyperbolic equations

DOI: 10.3233/ASY-181503

Journal: Asymptotic Analysis, vol. 112, no. 3-4, pp. 213-225, 2019