250 papers
This paper establishes quantitative Calderón-Zygmund estimates for 2D viscous Hamilton-Jacobi equations with natural gradient growth and applies them to prove the existence of classical solutions for stationary second-order Mean Field Games systems with defocusing power-law couplings, while also surveying existing regularity results and outlining open problems.
This paper establishes conditional stability for the backward problem of degenerate viscous Hamilton-Jacobi equations with general non-quadratic Hamiltonians using Carleman estimates and linearization, and proposes numerical identification algorithms based on the adjoint state method and Van Cittert iteration, validated by numerical tests.
This paper proves that balls are the unique open bounded domains satisfying the mean value property for polyharmonic functions by adapting Kuran's argument for harmonic functions and establishing a quantitative version of this rigidity result.
This paper establishes the -contraction property and time-asymptotic stability of monotone viscous-dispersive shock waves for the KdV-Burgers equation under arbitrarily large perturbations, providing uniform estimates with respect to viscosity and dispersion strengths.
This paper establishes the unique recovery of the location and time-dependent amplitude of a point source in the heat equation from sparse boundary flux measurements on unit balls in higher dimensions and simply connected smooth domains in two dimensions, utilizing a combination of spectral analysis, kernel properties, and complex analysis, and validates these theoretical findings through numerical experiments.
This paper presents two novel, short proofs for the sharp uniform-in-diffusivity mixing rate of passive scalars in parallel shear flows with weak molecular diffusion, utilizing stochastic integration-by-parts to establish optimality under minimal regularity and a dynamical systems approach to provide a new perspective on shear-induced mixing.
This paper extends the theoretical framework for estimating diffusive flux into stochastically gated tubes by deriving an explicit formula that remains accurate for non-narrow geometries and varying diffusivities, overcoming challenges related to complex 3D geometry and multiplicative noise.
This paper reviews rigorous results on the semiclassical behavior of the scattering data for a non-self-adjoint Dirac operator with oscillatory potential, utilizing exact WKB and Olver's methods to advance the understanding of the focusing cubic NLS equation via inverse scattering theory.
This paper establishes the global existence of smooth solutions and the finite-time formation of singularities for radially symmetric supersonic expanding waves in non-isentropic compressible Euler equations by introducing gradient variables to construct invariant domains and derive a priori estimates.
This paper establishes stability estimates for reconstructing the locations and time-dependent amplitudes of point sources in parabolic equations with non-self-adjoint elliptic operators from boundary observations, utilizing a novel combination of Carleman estimates, solution regularity, and explicit adjoint constructions across various spatial dimensions, supported by numerical reconstructions.
This paper establishes pointwise Wolff potential estimates for the gradient and Lipschitz regularity for solutions to nonlinear elliptic equations with measure data under Orlicz-type growth conditions, recovering known results for the singular -Laplace equation in the power-type case.
This paper establishes a rigorous two-way equivalence between the incompressible Navier-Stokes equations and the principle of minimum pressure gradient (PMPG), demonstrating that the former is mathematically identical to the instantaneous minimization of the pressure force required to enforce incompressibility, thereby offering a variational framework that generalizes classical Galerkin projections and provides new insights into flow stability and the vanishing-viscosity limit.
This paper resolves the Einstein-scalar field conformal constraint equations under spherically symmetric and harmonic assumptions, revealing that while solutions on compact manifolds like the sphere exhibit nonexistence and instability in near-CMC regimes, the equations are always solvable on Euclidean and hyperbolic manifolds, thereby supporting the conformal method's utility for asymptotically flat and hyperbolic initial data.
This paper establishes the uniqueness of singular radial potentials in Schrödinger operators by proving that infinitely many Dirichlet spectra satisfying a Müntz-type condition determine the potential globally, while two spectra from specific distinct angular momenta ensure local uniqueness near the zero potential, thereby refining previous results and confirming a conjecture by Rundell and Sacks.
This paper establishes strong convergence rates for semi-discrete and fully discrete finite element approximations of a fourth-order stochastic pseudo-parabolic equation driven by additive noise, supported by numerical experiments.
This paper establishes global well-posedness, scattering results, and polynomial stability for wave-type equations with singular potentials and data on by employing Yamazaki-type estimates on Lorentz spaces, fixed point arguments, and dispersive estimates within a weak- framework.
This paper establishes that solitons on non-compact metric graphs satisfying a specific topological assumption remain confined to their initial half-line and reflect off the graph's core, while proving the orbital stability of the unique ground state that exists only on the exceptional "bubble-tower" graph.
This paper establishes the first example of Batchelor's law for a passive scalar under deterministic forcing by proving that sufficiently smooth initial data in a specific time-periodic, Lipschitz velocity field converges to a limiting solution satisfying a cumulative form of the law.
This paper develops a linearized boundary control method to reconstruct unknown damping perturbations in the damped wave equation from the linearized Neumann-to-Dirichlet map, providing stability estimates and a validated numerical algorithm for constant backgrounds in any dimension while establishing increasing stability for non-constant backgrounds in dimensions three and higher.
This paper reviews and contrasts the long-time behavior of initial-boundary value problems for systems admitting Lax Pair formulations, illustrating cases where integrability ensures regular asymptotic behavior alongside instances where irregular, fractal-like chaos emerges, while connecting these findings to perturbed Lax Pair theory on the real line.