math.AP papers | Gist.Science

Regularization of the superposition principle: Potential theory meets Fokker-Planck equations

This paper advances the superposition principle for Fokker-Planck equations by constructing a full-fledged right Markov process under general measurability conditions, thereby resolving the open problem of establishing the strong Markov property and enabling new probabilistic solutions to the parabolic Dirichlet problem and flow constructions for both linear and nonlinear cases, including the generalized porous media equation.

Lucian Beznea, Iulian Cîmpean, Michael Röckner2026-03-06🔢 math

Besov regularity of solutions to the Dirichlet problem for the Bessel $(p,s)$ -Laplacian

This paper establishes global Besov regularity estimates for weak solutions to the Dirichlet problem of a fractional $p$ -Laplacian defined via the Riesz fractional gradient by combining Lions-Calderón spaces, Besov embeddings, and an adapted Nirenberg difference quotient method, yielding specific regularity indices that depend on the interplay between the order $s$ and the exponent $p$ in both superquadratic and subquadratic regimes.

Juan Pablo Borthagaray, Leandro M. Del Pezzo, José Camilo Rueda Niño2026-03-06🔢 math

The Extra Vanishing Structure and Nonlinear Stability of Multi-Dimensional Rarefaction Waves: The Geometric Weighted Energy Estimates

This paper establishes the nonlinear stability of multi-dimensional rarefaction waves for the compressible Euler equations by introducing a novel Geometric Weighted Energy Method that overcomes derivative loss issues through the identification of a hidden vanishing structure in the top-order derivatives of the characteristic speed.

Haoran He, Qichen He2026-03-06🔬 physics

Conditional asymptotic stability of solitary waves of the Euler-Poisson system on the line

This paper establishes the conditional asymptotic stability of solitary waves for the Euler-Poisson system on the line by combining virial inequalities and Kato smoothing to prove that solutions remaining close to a soliton converge to it as time approaches infinity.

Junsik Bae, Scipio Cuccagna, Masaya Maeda2026-03-06🔢 math

Existence and regularity for an entire Grushin-Choquard equation

This paper establishes the existence of a mountain pass solution and proves its global $L^q$ integrability and local Hölder continuity for an entire Choquard equation involving the Grushin operator on $\mathbb{R}^N$ .

Federico Bernini, Paolo Malanchini2026-03-06🔢 math

On spiral steady flows for the Couette-Taylor problem

This paper investigates steady incompressible viscous flows in a 3D cylindrical annulus with one stationary cylinder, explicitly determining all spiral-symmetric solutions and proving their stability against finite-energy perturbations for small boundary data, while highlighting a key analytical difference depending on which cylinder is fixed.

Edoardo Bocchi, Filippo Gazzola, Antonio Hidalgo-Torné2026-03-06🔢 math

Well-posedness of the heat equation in domains with topological transitions

This paper establishes the well-posedness of the heat equation with homogeneous Dirichlet boundary conditions in time-evolving domains undergoing topological transitions by introducing anisotropic space-time function spaces and applying the Babuška-Banach theorem to prove existence, uniqueness, and a priori estimates for weak solutions.

Maxim Olshanskii, Arnold Reusken2026-03-06🔬 physics

2D capillary liquid drops with constant vorticity: rotating waves existence and a conditional energetic stability result for rotating circles

This paper establishes the existence and conditional energetic stability of rotating wave solutions for two-dimensional capillary liquid drops with constant vorticity by utilizing a Hamiltonian framework, bifurcation theory, and critical point theory.

Giuseppe La Scala2026-03-06🔬 physics

Attenuation of long waves through regions of irregular floating ice and bathymetry

This paper presents a revised, energy-conserving theoretical model for the attenuation of long waves through regions of irregular floating ice and random bathymetry, which corrects previous over-predictions by utilizing ensemble averaging of transfer matrix eigenvalues and successfully reproduces key features of field data, including frequency-dependent attenuation rates and high-frequency roll-over effects.

Lloyd Dafydd, Richard Porter2026-03-05🔬 physics

On well-posedness and maximal regularity for parabolic Cauchy problems on weighted tent spaces

This paper establishes the well-posedness and maximal regularity of weak solutions to parabolic Cauchy problems with bounded, time-independent, uniformly elliptic coefficients in weighted tent spaces by extending singular integral operator theory via off-diagonal estimates and employing interior representation techniques to prove uniqueness.

Pascal Auscher, Hedong Hou2026-03-05🔢 math

On well-posedness for parabolic Cauchy problems of Lions type with rough initial data

This paper establishes a comprehensive well-posedness theory for parabolic Cauchy problems with time-independent, uniformly elliptic, bounded measurable complex coefficients, demonstrating that tempered distributions in homogeneous Hardy–Sobolev or Besov spaces serve as valid initial data for weak solutions with gradients in weighted tent spaces when source terms are of Lions' type.

Pascal Auscher, Hedong Hou2026-03-05🔢 math

Ill-posedness of the Boltzmann-BGK model in the exponential class

This paper demonstrates the ill-posedness of the BGK model by constructing both homogeneous and inhomogeneous solutions that instantly escape their initial solution spaces through temperature increases and polynomial spatial growth, respectively, highlighting a stark contrast with the stability of the Boltzmann equation.

Donghyun Lee, Sungbin Park, Seok-Bae Yun2026-03-05🔢 math

On regularity of solutions to the Navier--Stokes equation with initial data in $\mathrm{BMO}^{-1}$

This paper establishes that mild solutions to the incompressible Navier-Stokes equations with initial data in $\mathrm{BMO}^{-1}$ are weak*-continuous in time and that global solutions vanish in $\mathrm{BMO}^{-1}$ as time approaches infinity.

Hedong Hou2026-03-05🔢 math

Fractional Ito Calculus for Randomly Scaled Fractional Brownian Motion and its Applications to Evolution Equations

This paper defines a fractional Ito stochastic integral with respect to a randomly scaled fractional Brownian motion using an $S$ -transform approach, establishes the corresponding Ito formula, and applies it to investigate generalized time-fractional evolution equations.

Yana A. Butko, Merten Mlinarzik2026-03-05🔬 physics

Fujita-type results for the semilinear heat equations driven by mixed local-nonlocal operators

This paper establishes the Fujita-type critical exponents for semilinear heat equations driven by mixed local-nonlocal operators, demonstrating that the critical threshold is governed solely by the nonlocal component and thereby refining existing results for both forced and unforced cases.

Vishvesh Kumar, Berikbol T. Torebek2026-03-05🔢 math

Compact Sobolev embeddings of radially symmetric functions

This paper establishes a complete characterization of the compactness of Sobolev embeddings for radially symmetric functions on $\mathbb{R}^n$ and weighted balls within the general framework of rearrangement-invariant function spaces by developing novel techniques that overcome the limitations of previous methods restricted to domains of finite measure.

Zdeněk Mihula2026-03-05🔢 math

Blowup masses of Toda systems corresponding to the Weyl groups

This paper investigates the blowup phenomena of Toda systems, which generalize the Liouville equation via simple Lie algebras, by providing concrete examples of blowup masses that correspond to Weyl groups.

Zhaohu Nie2026-03-05🔬 physics

Well-posedness and long-time behavior of a bulk-surface Cahn--Hilliard model with non-degenerate mobility

This paper establishes the well-posedness, instantaneous separation, and long-time convergence to stationary states for a two-dimensional bulk-surface Cahn--Hilliard model with non-degenerate mobility and singular potentials, utilizing a novel regularity theory for bulk-surface elliptic systems to prove uniqueness and continuous dependence.

Jonas Stange2026-03-05🔬 physics

On the attenuation of waves through broken ice of randomly-varying thickness on water of finite depth

This paper extends a theoretical model of wave attenuation through broken floating ice of random thickness to finite water depths, utilizing multiple scales analysis to derive an explicit attenuation expression that predicts an eighth-power frequency dependence at low frequencies and shows strong agreement with numerical simulations and field measurements.