2517 papers
This collection explores the cutting edge of mathematical research, where abstract theories meet rigorous logic to solve complex problems. From pure number theory to applied statistics, these studies form the backbone of scientific discovery, offering new ways to model everything from climate patterns to artificial intelligence. While the original research can be dense, the insights here are fundamental to advancing our understanding of the universe.
Gist.Science monitors arXiv daily to bring you every new preprint in this field the moment it is published. We process each submission to provide both a clear, plain-language overview for general readers and a detailed technical summary for experts, ensuring that groundbreaking math is accessible to everyone. Below are the latest papers in Mathematics from arXiv, curated to help you stay ahead of the curve.
This paper establishes a trilinear Bourgain-space estimate for the derivative cubic term of the modified Zakharov--Kuznetsov equation on with specific input and output exponents, providing a self-contained dyadic proof to recover local well-posedness in for .
This paper establishes the uniqueness of viscosity solutions to the equation in a bounded domain for continuous non-positive functions by proving a comparison principle for the nonlocal infinity Laplace operator.
This paper establishes the small-data global well-posedness of the skew mean curvature flow for codimension-two submanifolds in () within the critical Besov space by reformulating the problem as a quasilinear Schrödinger equation and overcoming the lack of derivative margins through a novel combination of a div-curl lemma for low-high interactions and a quasilinear interaction Morawetz estimate for comparable and high-high frequency interactions.
This paper establishes the unique determination of potentials within a specific admissible class for the fractional Borg-Levinson inverse spectral problem, provided the fractional exponent lies in the interval .
This paper establishes the consistency and convergence rates of a Bayesian posterior distribution for the single-measurement fractional Calderón problem by employing rescaled Gaussian sieve priors and overcoming technical challenges related to the limited regularity of fractional elliptic problems.
This paper establishes error estimates for monotone numerical schemes approximating convex Hamilton-Jacobi equations on the -dimensional torus by deriving an bound of order one via the adjoint method and semiconcavity, which is then extended to all through interpolation with classical estimates.
This paper investigates the critical structure of axisymmetric Navier-Stokes equations with swirl by introducing new variables and proving a series of novel identities and estimates that exclude specific recurrence mechanisms while leaving open the possibility of meridional Type-II records and other critical behaviors.
This paper establishes a rigorous stability framework for a high-precision singular profile of the Euler equations on , reducing the proof of finite-time singularity to the verification of explicit estimates and computable constants.
This paper presents evidence for a stable finite-time singularity in the 3D Euler equations on by utilizing physics-informed neural networks to identify a self-similar blowup profile and establishing a framework to certify its nonlinear stability through linear damping and explicit estimates.
This paper establishes the local-in-time well-posedness of the two-dimensional unsteady Prandtl equations in Sobolev spaces for initial data with degenerate critical points and general outflow, demonstrating that Oleinik's monotonicity condition is not necessary for well-posedness and that zero shear stress does not inevitably cause boundary layer separation.