258 papers
This paper establishes the existence of traveling wave solutions, including non-monotone waves and front-pulse waves, for the two-species weak competition Lotka-Volterra system across all wave speeds , with a rigorous proof for the critical speed case and the first-time demonstration of front-pulse waves in the critical weak competition regime.
This paper establishes that limits of sequences of smooth maps between compact Riemannian manifolds with equi-integrable -Sobolev energy can always be strongly approximated by smooth maps, thereby extending Hang's density result to integer and providing proofs for higher-order and fractional Sobolev spaces as well as cases governed by the Bethuel-Demengel-Colon-Hélein cohomological criterion.
This paper investigates the existence, non-radiality, and full higher-order asymptotic behavior of positive rupture solutions to an elliptic MEMS equation featuring Hénon-type and external pressure terms near the origin.
This paper establishes the large-time stability and time-decay estimates for small perturbations around a time-periodic solution to the three-dimensional Navier-Stokes-Fourier system in the whole space, utilizing time-space integral estimates of the linearized semigroup in Besov spaces.
This paper formulates a bilinear local smoothing conjecture for Fourier integral operators in all dimensions , demonstrates that the linear conjecture implies this bilinear version, and establishes the conjecture for dimension and all odd dimensions .
This paper establishes the Sobolev regularity of a nonlinear function of the symmetric gradient for weak solutions to -Laplacian systems with Lipschitz coefficients and Orlicz-Sobolev data, utilizing uniform higher differentiability estimates derived from approximating problems with singular perturbations.
This paper establishes a new framework of Besov spaces on bounded domains with Neumann boundary conditions to prove the local well-posedness of the Navier-Stokes equations for initial data in a space that is strictly larger than any previously considered in bounded domains.
This paper investigates the existence, stability, and multiplicity of ground states and stationary solutions for the defocusing nonlinear Schrödinger equation on noncompact metric graphs, establishing that while small masses always yield stable ground states, large masses lead to non-existence in the subcritical regime, with specific sharp thresholds and bifurcation behaviors identified under -type vertex conditions.
This paper establishes the existence and nonexistence of ground states for mass-critical N-coupled attractive Fermi nonlinear Schrödinger systems in ring-shaped potentials based on the strength of interactions relative to a critical constant derived from a finite-rank Lieb-Thirring inequality, while also characterizing the mass concentration behavior of these states as the interaction strength approaches this critical threshold.
This paper establishes that Sobolev maps on the product of two Euclidean domains with invertible differentials preserving or swapping the factor spaces are necessarily split when the dimension , a result that fails for and for lower regularity spaces with .
This paper establishes the existence of regular global and exponential attractors with finite fractal dimension for the planar Coleman--Gurtin heat equation with memory and rough anisotropic diffusion encoded by a Beltrami coefficient, utilizing a combination of instantaneous smoothing techniques, maximal parabolic regularity, and quasiconformal estimates.
This paper constructs an arbitrary-order asymptotic expansion for the quantum evolution of coherent states in self-interacting bosonic field theories, refining previous leading-order results by applying Hepp's method to both spatially cutoff models and non-polynomial analytic interactions.
This paper establishes the functional framework and existence of weak solutions for quasilinear equations involving the fractional magnetic -Laplacian in three dimensions by employing variational methods and introducing a novel concentration compactness principle to address challenges posed by nonlocality, magnetic potentials, and critical nonlinearities.
This paper develops a spectral method to solve coupled kinetic and viscous half-space problems at network nodes, enabling the derivation of accurate macroscopic coupling conditions for the linearized BGK equation and its acoustic limit through detailed asymptotic analysis of interface layers.
This paper establishes the discrete Rubio de Francia extrapolation theorem for pairs of quasi non-increasing sequences with weights and provides a weight characterization for the boundedness of the generalized discrete Hardy averaging operator on such sequences within the space .
This paper extends Serrin's symmetry theorem to the anisotropic setting by proving that for a bounded indecomposable set of finite perimeter with specific regularity conditions, the existence of a weak solution to the anisotropic overdetermined torsion problem implies that the domain must be a translate and dilation of the Wulff shape.
This paper establishes the existence and multiplicity of solutions for an asymptotically linear fractional equation driven by the spectral fractional Laplacian with mixed Dirichlet-Neumann boundary conditions, utilizing pseudo-index theory when the nonlinear term is odd and specific parameter-eigenvalue relations hold.
This paper establishes the existence, uniqueness, and exponential mixing of an invariant measure for a stochastic generalized Constantin-Lax-Majda-DeGregorio model of turbulence featuring an anomalous enstrophy cascade, utilizing the Krylov-Bogoliubov argument and large viscosity conditions to advance the dynamical systems understanding of turbulent cascades.
This paper employs the Bahri-Coron barycenter method to establish the existence of a conformal metric with constant higher-order -curvature on specific Riemannian manifolds under a natural positivity condition, notably achieving this result without relying on a positive mass theorem.
The paper introduces GMM-PIELM, a probabilistic adaptive sampling framework that significantly improves the accuracy and conditioning of Physics-Informed Extreme Learning Machines for stiff PDEs by autonomously concentrating basis function centers in high-error regions like shock fronts, achieving orders-of-magnitude lower errors than baseline methods while retaining rapid closed-form training speeds.