math.AP papers | Gist.Science

Long finite time bubble trees for two co-rotational wave maps

This paper demonstrates that the energy-critical co-rotational wave maps equation from $\mathbb{R}^{2+1}$ into $\mathbb{S}^2$ admits finite-time blow-up solutions containing arbitrarily many concentric concentrating bubbles with alternating signs, thereby confirming that all scenarios predicted by the soliton resolution conjecture can occur.

Joachim Krieger, José M. PalaciosWed, 11 Ma🔢 math

Existence for the Discrete Nonlinear Fragmentation Equation with Degenerate Diffusion

This paper establishes the existence of global weak solutions for the discrete nonlinear fragmentation equation with degenerate diffusion in arbitrary spatial dimensions by utilizing weak $L^2$ estimates and compactness arguments, thereby extending previous results that were limited to one-dimensional domains with uniformly positive diffusion.

Saumyajit Das, Ram Gopal JaiswalWed, 11 Ma🔢 math

Large-time behaviour for coupled systems of Lotka-Volterra-type Fokker-Planck equations

This paper rigorously establishes the exponential convergence to equilibrium for a system of Fokker-Planck equations modeling predator-prey interactions by introducing Energy-type distances that reveal how the dissipative interaction term governs the emergence of stable equilibrium configurations.

Giuseppe Toscani, Mattia ZanellaWed, 11 Ma🔢 math

On Morawetz estimates for the elastic wave equation

This paper establishes Morawetz-type estimates for the elastic wave equation with singular weights, demonstrating that space-time weights $|(x,t)|^{-\alpha}$ allow for stronger singularities and weaker initial data regularity requirements compared to purely spatial weights $|x|^{-\alpha}$ .

Seongyeon Kim, Ihyeok SeoWed, 11 Ma🔢 math

Complex Scaling for the Junction of Semi-infinite Gratings

This paper presents and analyzes a complex scaling-based integral equation method that enables the efficient, high-order, and exponentially accurate numerical solution of wave scattering problems involving the junction of two semi-infinite periodic structures by analytically continuing the formulation into the complex plane to overcome slow kernel decay and prove its well-posedness.

Fruzsina J. Agocs, Tristan Goodwill, Jeremy HoskinsWed, 11 Ma🔢 math

Hyperbolic nonlinear Schrödinger equations on $\mathbb{R}\times \mathbb{T}$

This paper establishes sharp local well-posedness up to critical regularity and proves global existence with scattering for small initial data in critical Sobolev spaces for hyperbolic nonlinear Schrödinger equations on $\mathbb{R}\times\mathbb{T}$ , relying fundamentally on sharp endpoint Strichartz estimates.

Engin Basako\u{g}lu, Chenmin Sun, Nikolay Tzvetkov, Yuzhao WangWed, 11 Ma🔢 math

Non-concentration estimates for Laplace eigenfunctions on compact $C^{\infty}$ manifolds with boundary

This paper extends interior non-concentration estimates for Laplace eigenfunctions to the boundary of compact smooth manifolds with boundary, demonstrating that these bounds, combined with a generalized sup-norm estimate, immediately yield the sharp $O(\lambda^{\frac{n-1}{2}})$ $L^\infty$ bounds established by Grieser.

Hans Christianson, John A. TothWed, 11 Ma🔢 math

On some Sobolev and Pólya-Szegö type inequalities with weights and applications

This paper establishes new weighted Sobolev embedding theorems and a Pólya-Szegö type inequality derived from an isoperimetric problem to analyze a class of semilinear degenerate elliptic equations in a three-dimensional domain, thereby extending existing results to higher dimensions.

Trung Hieu Giang, Nguyen Minh Tri, Dang Anh TuanWed, 11 Ma🔢 math

Normal traces and applications to continuity equations on bounded domains

This paper establishes that the normal Lebesgue trace satisfies the Gauss-Green identity and occupies an intermediate regularity class between distributional and strong traces, enabling the proof of uniqueness for weak solutions to continuity equations on bounded domains under relaxed boundary regularity assumptions, while demonstrating that such assumptions remain necessary when characteristics enter the domain.

Gianluca Crippa, Luigi De Rosa, Marco Inversi, Matteo NesiWed, 11 Ma🔢 math

The Sommerfeld-Rellich Framework for Scattering on Hyperbolic Space: Far-Field Patterns and Inverse Problems

This paper establishes a complete time-harmonic scattering theory for hyperbolic space by introducing a hyperbolic Sommerfeld radiation condition and Rellich theorem to uniquely define far-field patterns, thereby solving direct scattering problems and initiating the study of inverse scattering for obstacles and media in this geometry.

Lu Chen, Hongyu LiuWed, 11 Ma🔢 math

On a fractional nonlinear Schrödinger equation with irregular coefficients. case: d<2s

This paper establishes the well-posedness of a cubic nonlinear Schrödinger equation with irregular coefficients in the regime $d<2s$ by introducing and proving the existence, uniqueness, and classical compatibility of "very weak solutions," while also validating these findings through numerical experiments.

Arshyn Altyby, Michael Ruzhansky, Mohammed Elamine Sebih, Niyaz TokmagambetovWed, 11 Ma🔢 math

Complex Dynamics of Wave-Character Transitions in Radially Symmetric Isentropic Euler Flows: Theory and Numerics

This paper investigates the qualitative dynamics and wave-character transitions in radially symmetric isentropic Euler flows across outward supersonic, subsonic, and inward supersonic regimes, establishing structural restrictions, identifying novel asymmetric transition mechanisms, deriving conditions for finite-time singularity formation, and validating these theoretical findings through Semi-Discrete Lagrangian-Eulerian numerical simulations.

Eduardo Abreu, Geng Chen, Faris El-Katri, Erivaldo LimaWed, 11 Ma🔢 math

Finite-energy solutions to Einstein-scalar field Lichnerowicz equations on complete Riemannian manifolds

This paper establishes the existence and nonexistence of finite-energy solutions to singular Einstein-scalar field Lichnerowicz equations on complete Riemannian manifolds with low-regularity coefficients, utilizing $\varepsilon$ -regularization, mountain pass arguments, and Harnack's inequality under specific spectral, geometric, and integrability conditions.

Bartosz Bieganowski, Pietro d'Avenia, Jacopo SchinoWed, 11 Ma🔢 math

Fast dynamo action on the 3-torus for pulsed-diffusions

This paper rigorously proves the fast dynamo conjecture for a pulsed-diffusion model on the 3-torus by constructing a specific hyperbolic velocity field and utilizing anisotropic Banach spaces to demonstrate that magnetic instability persists under small diffusivity.

Michele Coti Zelati, Massimo Sorella, David VillringerWed, 11 Ma🔢 math

On the simplicity of the sloshing eigenvalues

This paper proves that for sloshing problems defined by the Laplace equation with mixed boundary conditions on a smooth bounded domain, all eigenvalues become simple under small perturbations of the domain.

Marco Ghimenti, Anna Maria Micheletti, Angela PistoiaWed, 11 Ma🔢 math

Optimal Control in Age-Structured Populations: A Comparison of Rate-Control and Effort-Control

This paper contrasts the mathematical structures and optimality conditions of rate-control versus effort-control harvesting in age-structured populations, demonstrating how the multiplicative, aggregate-dependent nature of effort-control introduces nonlocal coupling in the adjoint system that fundamentally distinguishes it from the additive rate-control formulation.

Jiguang Yu, Louis Shuo WangWed, 11 Ma🔢 math

Steady States of Transport-Coagulation-Nucleation Models

This paper establishes the existence and qualitative properties of steady states for a nonlinear integro-differential equation modeling polymer dynamics involving nucleation, transport, and multiplicative coagulation, demonstrating that a sufficiently strong decay rate for large polymers prevents gelation despite the coagulation kernel's tendency to cause it in isolation.

Julia Delacour, Marie Doumic, Carmela Moschella, Christian SchmeiserWed, 11 Ma🔢 math

$\Gamma$ -convergence for nonlocal phase transitions involving the $H^{1/2}$ norm and surfactants

This paper establishes the compactness and $\Gamma$ -convergence of a nonlocal phase transition functional involving the $H^{1/2}$ norm and surfactants to a local perimeter-type energy that accounts for both the interfacial surfactant density and the total variation of the surfactant measure away from the interface.

Giuliana Fusco, Tim HeilmannWed, 11 Ma🔢 math

Asymptotic behavior of the solution with positive temperature in nonlinear 3D thermoelasticity

This paper establishes the global well-posedness and proves that solutions to the nonlinear three-dimensional thermoelasticity system with positive temperature globally converge to an equilibrium state with a uniform temperature distribution determined by energy conservation.

Chuang Ma, Bin GuoWed, 11 Ma🔢 math

Large-data solutions in multi-dimensional thermoviscoelasticity with temperature-dependent viscosities

This paper establishes the global existence of weak solutions for arbitrarily large initial data in a multi-dimensional quasilinear thermoviscoelastic system with temperature-dependent viscosity, extending previous one-dimensional results to higher dimensions without requiring smallness conditions on the data.