260 papers
This paper provides numerical evidence demonstrating that the Hopf bifurcation occurring at the upper marginal stability curve for various shear flows in the incompressible Navier-Stokes equations is subcritical.
This paper establishes a sharp regularity result in spatial variables for distributional solutions to the Navier-Stokes equations that satisfy the Prodi-Serrin condition, without requiring the solutions to belong to the local Leray-Hopf class.
This paper establishes that the singular set in the parabolic obstacle problem for general obstacles has a parabolic Hausdorff dimension of at most , extending a previous result limited to constant Laplacian obstacles by combining a truncated parabolic frequency formula with monotonicity estimates and an iterative argument.
This paper establishes an asymptotic expansion in inverse powers of time for the correlation functions of isometric extensions of volume-preserving Anosov flows defined on Abelian covers of closed manifolds.
This paper establishes the existence of two normalized solutions with a prescribed -norm for the stationary nonlinear Schrödinger equation with a radial potential in the mass-supercritical regime, utilizing Morse theory, spectral arguments, and radial blow-up analysis under minimal assumptions on the potential's sign, behavior at infinity, and regularity.
This paper establishes the exponential stability of the linearized viscous Saint-Venant equations in the norm by constructing an explicit diagonal quadratic Lyapunov function and deriving sufficient conditions on boundary parameters for small viscosities.
This paper introduces a stochastic nonlocal fractional reaction-diffusion model for tumour dynamics driven by multiplicative fractional Brownian motion, establishing well-posedness, deriving explicit blow-up time bounds and probabilities via a Doss-Sussmann transformation, and illustrating how anomalous diffusion and correlated noise jointly influence long-term tumour progression or extinction.
This paper establishes the existence of nontrivial nonnegative weak solutions to a semilinear Grushin-Schrödinger equation in with controlled potentials by proving the embedding of the associated energy space into a weighted Lebesgue space and deriving subsequent regularity results.
This paper demonstrates that, unlike the Casten-Holland and Matano theorem for interior reactions, nonconstant stable solutions for boundary reactions can exist in convex domains such as squares and regular polygons (but not circles), with their existence and the location of boundary singularities determined by a new renormalized energy function derived from the domain's conformal structure.
This paper establishes local Schauder estimates for flat viscosity solutions to a class of non-convex fully nonlinear elliptic PDEs with Dini continuous data and linear drift terms using geometric tangential techniques, while also deriving an Evans-Krylov type estimate and characterizing the nodal sets of such solutions.
This paper establishes a functional law of large numbers for a spatial model of Muller's ratchet, proving that the system converges to an infinite system of partial differential equations that rigorously determine population spreading speeds and demonstrate that deleterious mutations can indeed surf deterministic population waves.
This paper derives and analyzes a Fokker-Planck-type mean-field PDE model for stochastic reinforcement learning in market entry games, proving solution existence and demonstrating that the model captures aggregate learning and sorting phenomena with distinct time scales consistent with empirical evidence.
This paper applies the classical Lie symmetry method to a nonlinear heat-diffusion equation with variable coefficients to classify admitted symmetries, reduce the partial differential equation to ordinary differential equations, and construct invariant solutions for physically relevant cases such as Storm-type materials and power-law dependencies.
This paper extends the study of peeling properties for scalar fields to Dirac fields on Kerr spacetimes by combining Penrose conformal compactification with geometric energy estimates to define peeling via Sobolev regularity near null infinity and establish optimal initial data spaces, confirming that decay and regularity assumptions in Kerr yield the same regularity across null infinity as in Minkowski space for all angular momentum values.
This paper establishes the peeling property for tensorial Fackerell-Ipser and spin Teukolsky equations on Schwarzschild spacetime by combining conformal compactification with vector field techniques to derive energy estimates and determine optimal initial data ensuring asymptotic decay along radial geodesics.
This paper resolves a remaining open problem regarding far-field refraction in lossy negative refractive index materials by establishing the existence of weak solutions for two distinct relative refractive index cases using the Minkowski method and deriving a governing Monge-Ampère type inequality.
This paper establishes sharp large-time asymptotic formulas for the heat kernel on homogeneous trees and demonstrates that solutions to the heat equation with weighted initial data asymptotically factorize into the heat kernel and a -dependent mass function, a phenomenon distinct from the integer lattice case due to the specific influence of the tree's geometry.
This paper establishes optimal nontangential maximal function estimates and boundary regularity results for the Green function associated with second-order, homogeneous, constant-coefficient elliptic systems in the upper-half space, utilizing Agmon-Douglis-Nirenberg techniques and a specialized Divergence Theorem.
This paper establishes the existence of finite-time self-similar blow-up solutions for the inviscid generalized Surface Quasi-Geostrophic equation on and the upper half-plane by deriving and analyzing a one-dimensional reduction that captures the leading-order singular behavior, with results further supported by numerical simulations.
This paper rigorously establishes the convergence of global finite-energy weak solutions for the compressible Navier-Stokes system on a 3D torus with vacuum regions to an overdamped limiting system, where the momentum equation reduces to a stationary elliptic balance between pressure and viscous forces and the kinetic energy vanishes.