Article
Mathematics, Applied
Christian Zillinger
Summary: The article discusses linear inviscid damping in Gevrey regularity for compactly supported Gevrey regular shear flows in a finite channel, providing an alternative proof of stability using Fourier-based Lyapunov functional. The stability in L-2 by Fourier methods immediately upgrades to stability in Gevrey regularity for certain flows, even without assuming compact support.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2021)
Article
Mathematics
Daniel Oliveira da Silva, Alejandro J. Castro
Summary: This study establishes an asymptotic rate of decay for the spatial analyticity radius of solutions to the nonlinear wave equation with initial data in the analytic Gevrey spaces.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Computer Science, Theory & Methods
Thomas Kuehn, Martin Petersen
Summary: This paper introduces Gevrey spaces on the d-dimensional torus and studies the approximation numbers of their embeddings into L2. The dependence on the dimension of the underlying domain is emphasized, which is important for numerical treatment of high dimensional problems. The results provide guidance for handling high dimensional problems numerically.
JOURNAL OF COMPLEXITY
(2022)
Article
Mathematics, Applied
Yatao Li, Jitao Liu, Yanxia Wu
Summary: In this paper, we investigate the Cauchy problem of the inviscid lake equations in the Besov spaces for the first time and prove the global existence and uniqueness of the solutions.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Alexandre Arias Arias Junior, Alessia Ascanelli, Marco Cappiello
Summary: We prove the well-posedness of the Cauchy problem for a class of third-order quasilinear evolution equations with variable coefficients in projective Gevrey spaces. The considered class is closely related to several equations in Mathematical Physics such as the KdV and KdVB equations and some of their generalizations.
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES
(2023)
Article
Mathematics, Applied
Wilberclay G. Melo, Thyago S. R. Santos, Natielle dos Santos Costa
Summary: This paper establishes the existence of a unique mild solution for the anisotropic quasi-geostrophic equation and studies the decay rate and initial value conditions of the solution.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Dongfen Bian, Yan Guo, Ian Tice
Summary: In this study, a variational framework was developed to analyze the stability of the z-pinch system in the absence of viscosity effects, revealing that the z-pinch system is always unstable. Additionally, a sufficient condition for unbounded eigenvalues was discovered, leading to ill-posedness in the linearized MHD system.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2021)
Article
Mathematics, Applied
Weinan Wang
Summary: In this paper, we study the problem of analyticity up to the boundary for the 3D inviscid Boussinesq equations in a half space R-+(3). Furthermore, we prove the persistence of Gevrey regularity and obtain lower bounds on the radius of Gevrey regularity.
COMMUNICATIONS IN MATHEMATICAL SCIENCES
(2022)
Article
Mathematics
Siqi Ren, Luqi Wang, Dongyi Wei, Zhifei Zhang
Summary: In this paper, we prove the inviscid damping and vortex axisymmetrization for the linearized Euler equation around the radially symmetric, strictly monotonic vorticity distribution via the vector field method. One of the key ingredients is to establish the limiting absorption principle for the Rayleigh equation. Compared with shear flows in a channel, the main difficulty comes from the degeneration of the pipe flow at the original point and infinity.
JOURNAL OF FUNCTIONAL ANALYSIS
(2023)
Article
Mathematics
Stevan Pilipovic, Nenad Teofanov, Filip Tomic
Summary: New spaces of ultradistributions were investigated as dual spaces of test functions with logarithmic-type growth, proving that boundary values of analytic functions with corresponding growth rate towards the real domain are also ultradistributions. The classical stability condition under ultradifferential operators was replaced by a weaker condition controlled by an additional parameter, requiring new techniques in the proofs. Wave front sets were discussed as an application of the theory.
Article
Mathematics, Applied
Hantaek Bae, Woojae Lee
Summary: This paper presents mathematical results for models of phase separation of self-propelled particles, demonstrating the existence of a unique global in-time solution, Gevrey regularity, and decay properties with small initial data in scaling-invariant spaces.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
Article
Mathematics
Veronique Fischer, Michael Ruzhansky, Chiara Alba Taranto
Summary: This paper defines and studies the Gevrey spaces associated with a Hormander family of vector fields and its corresponding sub-Laplacian. It shows natural relations between the various Gevrey spaces on general manifolds and particular properties on Lie groups with polynomial growth of volume. In the cases of the Heisenberg group and SU(2), it is demonstrated that all descriptions coincide.
MATHEMATISCHE NACHRICHTEN
(2021)
Article
Mathematics
Slim Ibrahim, Quyuan Lin, Edriss S. Titi
Summary: This study investigates the dynamics of inviscid primitive equations with rotation, proving their ill-posedness in Sobolev spaces and suggesting that a suitable space for well-posedness is Gevrey class of order s = 1.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Engineering, Electrical & Electronic
Zharilkassin Iskakov, Kuatbay Bissembayev, Nutpulla Jamalov, Azizbek Abduraimov
Summary: This study investigates the dynamics of a gyroscopic rigid rotor with linear and nonlinear damping and stiffness, showing that joint linear and nonlinear damping significantly suppresses vibration amplitudes and affects bistability regions, and proposing a methodology to determine coefficients of support material properties. Damping also impacts stability of motion, with linear damping shifting instability boundaries and nonlinear cubic damping potentially eliminating them. The varying amplitude method is used to analyze system response with nonlinear effects on frequency response.
Article
Mathematics
R. O. B. E. R. T. A. Bianchini, Michele Coti Zelati, M. I. C. H. E. L. E. Dolce
Summary: We investigate the linear stability of shears near the Couette flow for a class of 2D incompressible stably stratified fluids. Our main result is about nearly optimal decay rates for perturbations of stationary states whose velocities are monotone shear flows and have an exponential density profile. These results also apply to the Boussinesq equations and hold under the celebrated Miles-Howard criterion.
INDIANA UNIVERSITY MATHEMATICS JOURNAL
(2022)
