Asymptotic Analysis - Volume 139, issue 1-2

Authors: Pelinovsky, Dmitry E. | Sobieszek, Szymon

Article Type: Research Article

Abstract: Ground state of the energy-critical Gross–Pitaevskii equation with a harmonic potential can be constructed variationally. It exists in a finite interval of the eigenvalue parameter. The supremum norm of the ground state vanishes at one end of this interval and diverges to infinity at the other end. We explore the shooting method in the limit of large norm to prove that the ground state is pointwise close to the Aubin–Talenti solution of the energy-critical wave equation in near field and to the confluent hypergeometric function in far field. The shooting method gives the precise dependence of the eigenvalue parameter versus …the supremum norm. Show more

Keywords: Gross–Pitaevskii equation, ground state, energy-critical case, shooting method

DOI: 10.3233/ASY-241897

Citation: Asymptotic Analysis, vol. 139, no. 1-2, pp. 1-29, 2024

Authors: Kassan, Mouna | Carbou, Gilles | Jazar, Mustapha

Article Type: Research Article

Abstract: In this paper, we establish the existence of global-in-time weak solutions for the Landau–Lifschitz–Gilbert equation with magnetostriction in the case of mixed boundary conditions. From this model, we derive by asymptotic method a two-dimensional model for thin ferromagnetic plates taking into account magnetostrictive effects.

Keywords: Ferromagnetism, magnetostriction, weak solutions, thin plates

DOI: 10.3233/ASY-241899

Citation: Asymptotic Analysis, vol. 139, no. 1-2, pp. 31-59, 2024

Authors: Liu, Jitao | Wang, Shasha | Xu, Wen-Qing

Article Type: Research Article

Abstract: Recently, Niche [J. Differential Equations, 260 (2016), 4440–4453] established upper bounds on the decay rates of solutions to the 3D incompressible Navier–Stokes–Voigt equations in terms of the decay character r ∗ of the initial data in H 1 ( R 3 ) . Motivated by this work, we focus on characterizing the large-time behavior of all space-time derivatives of the solutions for the 2D case and establish upper bounds and lower bounds on their decay rates by making use of the decay character and Fourier splitting …methods. In particular, for the case − n 2 < r ∗ ⩽ 1 , we verify the optimality of the upper bounds, which is new to the best of our knowledge. Similar improved decay results are also true for the 3D case. Show more

Keywords: Incompressible Navier–Stokes–Voigt equations, decay characterization, Fourier splitting, large-time behavior

DOI: 10.3233/ASY-241900

Citation: Asymptotic Analysis, vol. 139, no. 1-2, pp. 61-87, 2024

Authors: Huo, Wenwen | Teng, Kaimin | Zhang, Chao

Article Type: Research Article

Abstract: We consider the Cauchy problem for the 3-D incompressible Navier–Stokes–Allen–Cahn system, which can effectively describe large deformations or topological deformations. Under the assumptions of small initial data, we study the global well-posedness and time-decay of solutions to such system by means of pure energy method and Fourier-splitting technique.

Keywords: Navier–Stokes–Allen–Cahn, global well-posedness, time-decay, Fourier-splitting

DOI: 10.3233/ASY-241901

Citation: Asymptotic Analysis, vol. 139, no. 1-2, pp. 89-109, 2024

Authors: Nika, Grigor | Muntean, Adrian

Article Type: Research Article

Abstract: We derive effective models for a heterogeneous second-gradient elastic material taking into account chiral scale-size effects. Our classification of the effective equations depends on the hierarchy of four characteristic lengths: The size of the heterogeneities ℓ , the intrinsic lengths of the constituents ℓ SG and ℓ chiral , and the overall characteristic length of the domain L. Depending on the different scale interactions between ℓ SG , ℓ chiral , ℓ , and L we obtain either an …effective Cauchy continuum or an effective second-gradient continuum. The working technique combines scaling arguments with the periodic homogenization asymptotic procedure. Both the passage to the homogenization limit and the unveiling of the correctors’ structure rely on a suitable use of the periodic unfolding operator. Show more

Keywords: Second-gradient elasticity, scale-size effects, partial scale separation, chirality, multi-continuum homogenization

DOI: 10.3233/ASY-241902

Citation: Asymptotic Analysis, vol. 139, no. 1-2, pp. 111-137, 2024