Journal: SIAM Journal on Mathematical Analysis

Abbreviation

SIAM j. math. anal.

Publisher

SIAM

Journal Volumes

ISSN

0036-1410
1095-7154

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Publications 1 - 10 of 40
  • Quantitative Estimates for Stress Concentration of the Stokes Flow Between Adjacent Circular Cylinders
    Item type: Journal Article
    Ammari, Habib; Kang, Hyeonbae; Kim, Do Wan; et al. (2023)
    SIAM Journal on Mathematical Analysis
    When two inclusions with high-contrast material properties are located close to each other in a homogeneous medium, stress may become arbitrarily large in the narrow region between them. In this paper, we investigate such stress concentration in the two-dimensional Stokes flow when inclusions are the two-dimensional cross sections of circular cylinders of the same radii and the background velocity field is linear. We construct two vector-valued functions which completely capture the singular behavior of the stress and derive an asymptotic representation formula for the stress in terms of these functions as the distance between the two cylinders tends to zero. We then show, using the representation formula, that the stress always blows up by proving that either the pressure or the shear stress component of the stress tensor blows up. The blow-up rate is shown to be \(\delta^{-1/2}\), where \(\delta\) is the distance between the two cylinders.
  • Some new well-posedness results for continuity and transport equations, and applications to the chromatography system
    Item type: Journal Article
    Ambrosio, Luigi; Crippa, Gianluca; Figalli, Alessio; et al. (2009)
    SIAM Journal on Mathematical Analysis
  • Asymptotic Analysis of the SVD for the Truncated Hilbert Transform with Overlap
    Item type: Journal Article
    Alaifari, Rima; Defrise, Michel; Katsevich, Alexander (2015)
    SIAM Journal on Mathematical Analysis
  • Effective Medium Theory for Acoustic Waves in Bubbly Fluids near Minnaert Resonant Frequency
    Item type: Journal Article
    Ammari, Habib; Zhang, Hai (2017)
    SIAM Journal on Mathematical Analysis
  • Local Existence of Smooth Solutions for the Semigeostrophic Equations on Curved Domains
    Item type: Journal Article
    Silini, Lauro (2023)
    SIAM Journal on Mathematical Analysis
    We prove local-in-time existence and uniqueness of smooth solutions to the semigeostrophic equations in the general setting of smooth, bounded, and simply connected domains of R-2 endowed with an arbitrary conformally flat metric and nonvanishing Coriolis term. We present a construction taking place in Eulerian coordinates, avoiding the classical reformulation in dual variables used in the flat case with constant Coriolis force but lacking in this general framework.
  • On the Vanishing Viscosity Limit of Statistical Solutions of the Incompressible Navier–Stokes Equations
    Item type: Journal Article
    Fjordholm, Ulrik S.; Mishra, Siddhartha; Weber, Franziska (2024)
    SIAM Journal on Mathematical Analysis
    We study statistical solutions of the incompressible Navier-Stokes equation and their vanishing viscosity limit. We show that a formulation using correlation measures as in [U. S. Fjordholm, S. Lanthaler, and S. Mishra, Arch. Ration. Mech. Anal., 226 (2017), pp. 809-849] and moment equations is equivalent to statistical solutions in the Foiaş-Prodi sense. Under the assumption of weak scaling, a weaker version of Kolmogorov's self-similarity at small scales hypothesis that allows for intermittency corrections, we show that the limit is a statistical solution of the incompressible Euler equations. To pass to the limit, we derive a Kármán-Howarth-Monin relation for statistical solutions and combine it with the weak scaling assumption and a compactness theorem for correlation measures from [U. S. Fjordholm et al., Math. Models Methods Appl. Sci., 30 (2020), pp. 539-609].
  • Fractional Space-Time Variational Formulations of (Navier--) Stokes Equations
    Item type: Journal Article
    Schwab, Christoph; Stevenson, Rob (2017)
    SIAM Journal on Mathematical Analysis
  • Spectral Theory of Twisted Bilayer Graphene in a Magnetic Field
    Item type: Journal Article
    Becker, Simon; Zhu, Xiaowen (2025)
    SIAM Journal on Mathematical Analysis
    In this article, we study the Bistritzer-MacDonald model with external magnetic field. We study the spectral properties of the Hamiltonian in an external magnetic field with particular emphasis on the flat band of the chiral model at magic angles. Our analysis includes different types of tunneling potentials between layers, the so-called limits chiral and antichiral. One novelty of our article is that we show that using a magnetic field one can discriminate between flat bands of different multiplicities, as they lead to different Chern numbers in the presence of magnetic fields, while for zero magnetic field their Chern numbers always coincide.
  • Continuity of Multimarginal Optimal Transport with Repulsive Cost
    Item type: Journal Article
    Colombo, Maria; Di Marino, Simone; Stra, Federico (2019)
    SIAM Journal on Mathematical Analysis
  • Analytic Regularity for the Incompressible Navier-Stokes Equations in Polygons
    Item type: Journal Article
    Marcati, Carlo; Schwab, Christoph (2020)
    SIAM Journal on Mathematical Analysis
    In a plane polygon P with straight sides, we prove analytic regularity of the Leray-Hopf solution of the stationary, viscous, and incompressible Navier-Stokes equations. We assume small data, analytic volume force, and no-slip boundary conditions. Analytic regularity is quantified in so-called countably normed, corner-weighted spaces with homogeneous norms. Implications of this analytic regularity include exponential smallness of Kolmogorov N-widths of solutions, exponential convergence rates of mixed hp-discontinuous Galerkin finite element and spectral element discretizations, and model order reduction techniques. © 2020 Society for Industrial and Applied Mathematics.
Publications 1 - 10 of 40