261 papers
This paper proves the absence of anomalous dissipation for passive scalars driven by random divergence-free autonomous vector fields in Hölder classes with regularity by utilizing dimension-theoretic arguments rather than commutator estimates, thereby establishing that anomalous regularization does not occur for this class of fields.
This paper establishes a refined Nash stratification inequality for planar domains with connected horizontal cross-sections and applies it to prove global regularity for the 2D Patlak–Keller–Segel chemotaxis model coupled with Darcy fluid flow, demonstrating that arbitrarily weak buoyancy coupling suppresses finite-time singularities even for large initial data and complex geometries.
This paper establishes the global existence, uniform boundedness, and scattering of solutions for an energy-subcritical defocusing nonlinear Schrödinger equation in with inhomogeneous nonlinear damping and trapping potential by introducing a novel virial-modified energy to overcome the loss of energy monotonicity caused by spatially dependent damping.
This paper proves that the grand canonical Gibbs state of an inhomogeneous two-dimensional interacting Bose gas converges to the renormalized Euclidean field theory in the high-density, short-range interaction limit, overcoming significant mathematical challenges posed by the need for divergent counterterm functions rather than simple scalars due to the presence of a trapping potential.
This paper establishes the local-in-time well-posedness of smooth classical solutions to the vacuum free boundary problem of the viscous Saint-Venant system for shallow waters by utilizing new higher-order weighted energy functionals and estimates to handle the degeneracy near the moving boundary.
This paper establishes that homogenisation and renormalisation commute for the two-dimensional periodic generalised parabolic Anderson model by introducing a novel solution ansatz to handle variable coefficients and demonstrating that the standard model can be constructed via para-controlled calculus without commutator estimates.
This paper establishes the global existence and long-time convergence to flat interface solutions for the moving interface problem coupling the Navier-Stokes equations with a linear wave equation, demonstrating that initial data sufficiently close to equilibrium leads to stable fluid-structure interactions even in the presence of gravity.
This paper establishes Runge-type approximation results for solutions to linear partial differential equations with constant coefficients on spaces of smooth Whitney jets, providing geometric characterizations of density conditions for elliptic, parabolic, and wave operators, and applying these findings to the approximation of holomorphic functions on specific planar domains.
This paper establishes that for a mathematical model of tuberculosis granuloma formation, solutions with sufficiently small initial data exist globally and converge exponentially to the disease-free equilibrium when and the basic reproduction number .
This paper establishes the rigorous convergence of hyperbolic approximations to various higher-order PDEs, including the KdV and Kuramoto-Sivashinsky equations, by proving that weak solutions of the approximations converge to smooth solutions of the limiting problems, a result supported by numerical evidence.
This paper establishes the well-posedness and -based Sobolev regularity for vector-valued fluid dynamics PDEs, including Stokes and Navier–Stokes equations, on closed manifolds of minimal regularity by developing a parametrization-free variational approach that decouples velocity and pressure variables.
This paper establishes Lipschitz and Hölder stability for semi-discrete inverse source and Cauchy problems associated with stochastic parabolic equations in arbitrary dimensions by deriving and applying three new global Carleman estimates for the semi-discrete stochastic parabolic operator.
This paper presents a novel, fully closed, and hyperbolic two-fluid model for compressible two-phase flows derived via a new Stationary Action Principle, which introduces the interfacial work to ensure physical soundness across all flow topologies and provides a robust foundation for numerical simulations.
This paper establishes weak and strong elliptic Harnack inequalities for mixed local and nonlocal -energy forms on metric measure spaces by employing the De Giorgi--Nash--Moser method under axiomatic assumptions including the Poincaré and cutoff Sobolev inequalities.
This paper establishes the non-uniqueness of positive solutions for Cauchy problems of supercritical semilinear heat equations by proving that the existence of a positive radial singular stationary solution guarantees at least two distinct solutions starting from that singular initial data.
This paper establishes that for certain polarized degenerations of Calabi-Yau manifolds near an intermediate complex structure limit, the potential -convergence of the corresponding collapsing Ricci-flat Kähler metrics can be improved to metric convergence on a generic region.
This paper constructs probabilistically strong, strictly dissipative solutions to the three-dimensional Euler equations with additive noise that satisfy the local energy inequality, and uses these results to establish non-unique ergodicity for the forced system.
This paper establishes the first rigorous Nekhoroshev-type stability results for ultra-differentiable solutions of non-local semilinear Schrödinger equations without external parameters by employing rational normal forms and a novel global vector field norm, achieving optimal stability times under Gevrey regularity assumptions.
This paper investigates the total population levels in heterogeneous environments with directed diffusion for any power-law relationship between intrinsic growth rate and carrying capacity, disproving the existence of a critical exponent that determines population prevalence over carrying capacity and analyzing how the total population depends on the diffusion coefficient under a generalized dispersal strategy.
This paper analyzes a mechanochemical model of pattern formation in regenerating tissue spheroids, demonstrating that a feedback loop between mechanical stretching and morphogen production, coupled with global strain conservation, robustly generates stable single-peaked patterns through specific bifurcation structures without requiring a second diffusible inhibitor.