New papers on Analysis & PDEs
445 new papers on analysis & pdes in the last 7 days, within Math & statistics. These are the 50 Pipette rates most worth reading, with the main result in the authors' own words.
The best of the week
Messaging strategies and the emergence of echo chambers in collective decision-making
Using methods from nonlinear dynamics, we show that either of these constraints can cause collective accuracy to become extremely sensitive to the weight individuals place on the information they receive from others.
Peer-reviewed journalNonlinear Landau damping for the unconfined Vlasov-Poisson system in 2D
We prove nonlinear Landau damping for the two-dimensional Vlasov--Poisson system in the unconfined Euclidean setting near the homogeneous Poisson equilibrium \[ \mu(v)=\frac{1}{2\pi}(1+|v|^2)^{-3/2}.
PreprintClaims a big stepInfinite cascades for the defocusing cubic half-wave equation on the torus
We construct global solutions of the periodic defocusing cubic half-wave equation whose norms grow exponentially as for every .
PreprintClaims a big stepBlow-up for energy supercritical defocusing nonlinear Schr\"odinger equations in dimensions three, four and five
We prove finite time blow-up from smooth, radial, compactly supported initial data for the energy supercritical defocusing nonlinear Schr\"odinger equation in , for .
PreprintClaims a big stepLyapunov stability of polynomial vector fields is undecidable
We show that there are integers and odd such that no algorithm can decide, from the rational coefficients of a homogeneous polynomial vector field F of degree in dimension , whether the origin is Lyapunov stable for .
PreprintClaims a big stepA new type of deterministic Salem sets and its spectrality
For all , we provide a new deterministic construction of Cantor sets whose Fourier dimension and Hausdorff dimension are both equal to .
PreprintClaims a big stepSolution of the Mumford-Shah conjecture
We present a compact-translation argument for the classification of planar Mumford--Shah generalized global minimizers.
PreprintClaims a big stepAsymptotic Balance and Structural Rigidity in the Riemann Zeta Function
Consequently, every nontrivial zero must satisfy Re(s)=1/2.
Preprint with a published versionBold claims, read criticallyClaims a big stepStable De Giorgi conjecture of the Allen--Cahn equation in
We prove that every bounded stable entire solution of the Allen--Cahn equation in is one-dimensional.
PreprintClaims a big stepThe Solution to Agmon's Conjecture for the polylaplacian
We show that this is indeed the case for the polyharmonic operator of arbitrary order in , , even in geometrically rough domains permitting singularities beyond the scope of the existing theory of higher-order elliptic boundary value problems.
PreprintClaims a big stepSmooth and swirling steady vortex rings near the Hill--Norbury family
We confront the desingularization question, both within the swirl-free solution subspace and upon admitting swirl, and prove that each member of the Hill--Norbury family of sufficiently small flux is the limit of traveling-wave solutions to the Euler equations that are smooth to infinite order and have compact toroidal vorticity support.
PreprintClaims a big stepA counterexample to Eremenko's conjecture
This disproves the conjecture.
PreprintExplicit diagonalization of the linearized Calder\'on problem on the disk: multiplicity normalization and exponential spectral attenuation
We obtain an explicit continuous spectral diagonalization of its normal operator and hence a generalized singular system for the linearized forward map.
PreprintClaims a big stepGlobal flows for the cubic nonlinear Schr\"odinger equation without decay assumptions
As a principal application, we prove global well-posedness on for both signs, with finite-time bounds and locally Lipschitz dependence on initial-data norm balls.
PreprintClaims a big stepRegular Solutions of the Stationary Navier-Stokes Equations in Arbitrarily High Dimensions
Here we answer this question and obtain the existence of regular solutions to the stationary Navier--Stokes equations in arbitrarily high dimensions.
PreprintClaims a big stepCritical thresholds for the damped wave system with mixed product-type nonlinearities
We have succeeded in determining the critical curve, formulated in terms of the power exponents of nonlinearities, for the global (in time) existence of small data mild solutions and the nonexistence of global mild solutions.
PreprintClaims a big stepSelection of critical solutions in non-monotone vanishing discount problems
This provides the first mechanism for selecting multiple critical solutions in vanishing discount problems beyond the classical monotonicity framework, showing that different families of Mather measures yield different limiting critical solutions.
PreprintClaims a big stepFunctional dynamic mode decomposition: Learning infinite-dimensional systems from data
We extend projected and exact DMD to infinite-dimensional systems.
PreprintLipschitz-free spaces are strongly unique preduals
We prove that the Lipschitz-free space is the strongly unique isometric predual of for every metric space , solving a longstanding open problem of Weaver.
PreprintClaims a big stepGlobal well-posedness and scattering for the three-dimensional focusing energy-critical NLS
We prove global well-posedness and scattering for the three-dimensional focusing energy-critical NLS below the ground-state energy and gradient thresholds, confirming the threshold conjecture in dimension three.
PreprintLow Mach number limit around the planar diffusion wave for 3D Navier-Stokes-Fourier equations
For the well-prepared regime, the solutions of compressible NSF equations converge to a planar diffusion wave solution globally in time as the Mach number tends to zero, where the difference between the states at the far fields is independent of the Mach number.
PreprintClaims a big stepComplete integrability of the Calogero--Sutherland DNLS equation on
We establish the complete integrability of the defocusing Calogero--Sutherland derivative nonlinear Schr\"odinger equation \begin{equation}\label{CS-abstract}\tag{CS} i\partial_t u +\partial_x^2 u + 2i u \partial_x \Pi\!\left(|u|^2\right)=0,\qquad x\in\mathbb T, \end{equation} by constructing a nonlinear Fourier transform \begin{equation*} \Phi : u\in L^2_+(\mathbb T)\mapsto\ (\zeta_n(u))_{n\geq 0}\in \ell^2(\mathbb N_0),\qquad \zeta_n(u)=\sqrt{\gamma_n(u)}\;e^{ i\arg\langle u\mid f_n\rangle}, \end{equation*} built from the eigenvalues , the spectral gaps and the eigenfunctions of the Lax operator .
PreprintIncompressible Navier-Stokes Limit of the Relativistic Boltzmann Equation with the Optimal Convergence Rate
By using spectral analysis, we establish the convergence of the classical solution to the relativistic Boltzmann equation to that of the incompressible Navier-Stokes system, and give for the first time the optimal convergence rate and a precise estimate of the initial layer.
PreprintLearning Operators of Geometry with an Interface Autoencoder
In this paper, we first establish an approximation theorem for continuous operators between general state sets.
PreprintComparison and Almost Finiteness for Actions of Amenable Groups
We prove that every action of a countably infinite discrete amenable group on a nonempty compact Hausdorff zero-dimensional space has dynamical comparison, without assuming minimality, freeness, or metrizability.
PreprintAbsence of bounded-orbit wandering domains
We prove that transcendental entire functions do not have bounded-orbit wandering domains.
PreprintBounded-orbit wandering domains do not exist
This paper establishes that transcendental entire functions do not have wandering Fatou components whose forward orbit is bounded.
PreprintDissipative Evolutions in Metric Spaces
We study a novel class of evolution variational inequalities (EVI) driven by bifunctions defined on a subset of a metric space and satisfying a natural dissipativity condition We provide general conditions for existence, stability, regularity, approximation and asymptotic behavior of solutions, by proposing a metric framework that generalizes the classical structure of evolutions driven by monotone operators in Hilbert spaces.
PreprintMean field games with Hormander diffusions
We establish the well-posedness of the MFG systems in intrinsic Holder spaces, which describes the Nash equilibria for a differential game with infinitely many small players.
PreprintGlobal Well-Posedness of Strong Solutions to the Two-Dimensional Compressible Nematic Liquid Crystal Flows with Large Initial Data and Vacuum
Under the assumptions that the shear viscosity is a positive constant and that the bulk viscosity is given by with , we establish the global existence and uniqueness of strong solutions.
PreprintDesigning collective behaviour within a fixed coarse-grained description
Here we develop a method to identify and use such variations for collective-state design.
PreprintData-Driven Control in Infinite-Dimensional Spaces: Fundamental Lemma and Applications
This paper establishes a theoretical foundation for data-driven control in infinite-dimensional spaces by extending the notions of persistency of excitation, data informativity, and Willems' fundamental lemma. These extensions enable their direct application to systems governed by partial differential equations and delay differential equations.
PreprintWave propagation of a non-conservative compressible two-fluid model with different pressures
In sharp contrast, under unequal pressure, the stationary diffusion wave consists of two Huygens waves propagating at different speeds--a novel phenomenon absent in the classical Navier-Stokes context.
PreprintGeneric Structural Stability for Riemann Solutions to Systems of Hyperbolic Conservation Laws
This paper proves generic structural stability for Riemann solutions to systems of hyperbolic conservation laws in one spatial dimension.
PreprintThe Zygmund conjecture and Rey's exponential integrability conjecture
We prove the Zygmund conjecture in all parameters: the maximal operator associated with products of cubes with side lengths , where is any positive coordinatewise nondecreasing function, satisfies the weak estimate for every .
PreprintEscape, Oscillatory Relapse or Elimination: A Geometric Blow-up Analysis of a Tumour Model with Singular Bifurcations
In this paper, we recast these findings through the lens of geometric singular perturbation theory (GSPT) and the blow-up method, establishing a formal mathematical foundation for these phenomena.
PreprintThe Coulhon--Duong conjecture for the Riesz transform on complete Riemannian manifolds
We prove that its Riesz transform is of weak type , with constant for real-valued functions.
PreprintThe r-Safety Reserve and Adaptive Kinematic Smoothing for Car-Following Transitions
This paper develops such a connection through r-Safety and Adaptive Kinematic Smoothing (AKS).
PreprintReal-world useThe H\"older interpolative gap bound for degenerate parabolic double phase problems
If the solution itself is H\"older continuous with exponent , we prove higher integrability of its gradient under the gap condition together with .
PreprintObservable Lyapunov Exponents for Globally Coupled Maps in the Mean-Field Limit
Our main result shows that, for a broad class of symmetric macroscopic observables, these exponents turn out to be determined by the linearisation of the self-consistent transfer operator, which is the nonlinear operator governing the evolution of the population distribution.
PreprintPropagation of opinions on a network. Convergence, spreading speed and patterns in the Daley-Kendall model
We prove that the solutions converge and we study their asymptotic equilibrium.
PreprintFaber-Walsh field expansions for the planar conductivity problem with multiple inclusions
We derive an explicit Faber-Walsh representation for the planar conductivity problem with finitely many disjoint inclusions of general shape and independently chosen positive conductivities.
PreprintGlobal Existence and Large-Time Behavior of Strong Solutions to the Two-Dimensional Compressible Nematic Liquid Crystal Flows with Large Initial Data and Vacuum
For initial data allowing vacuum, we establish the global existence and uniqueness of strong solutions without any restrictions on the size of the initial data.
PreprintComplete characterization of planar linearizability and optimal conjugacy regularity
We establish a complete characterization of local linearizability for planar diffeomorphisms.
PreprintGlobal Exponential Stabilization of a 3D Nonholonomic Vehicle in Spherical Coordinates
To overcome this obstruction, we exploit the geometric singularity of spherical coordinates to design a backstepping continuous, time-invariant feedback law that exponentially stabilizes a 3D nonholonomic vehicle actuated solely by forward surge velocity, pitch rate, and yaw rate.
PreprintOrthonormal Strichartz estimates for the Schr\"odinger equations with Hamiltonian on Wiener amalgam spaces
We then extend these improved Strichartz estimates from a single initial datum to systems of orthonormal families, providing, to the best of our knowledge, the first results in this direction in the setting of Wiener amalgam spaces.
PreprintA priori regularity of the reverse heat flow and dimension-dependent complexity of higher-order diffusion samplers
We establish arbitrary-order a priori regularity estimates for the reverse heat flow in the Ornstein--Uhlenbeck setting, that is, for the probability-flow ODE of score-based diffusion models.
PreprintVoltage and current density in a rectangle with point in- and ejection via Green's functions and -analysis
We present an exact and computationally very efficient analytic formula of the potential and the magnitude of the current density in a rectangle.
PreprintCompartmental Epidemiological Models: Discussing Fundamental Elements via the SIR Model
We present a didactic treatment of compartmental disease spread modeling centered on the SIR framework, aimed at mathematics education.
Preprint with a published versionGlobal regularity for the unidirectional Euler-alignment system with supercritical dissipation
We prove global well-posedness of the periodic unidirectional Euler-alignment system in every dimension for supercritical dissipation of order and arbitrary non-vacuum initial data in the Sobolev class of the local theory.
Preprint