271 papers
This paper proves the -convergence of the time-splitting scheme to the unique global strong solution of the nonlinear Dirac equation in 1+1 dimensions by establishing pointwise estimates, constructing a modified Glimm-type functional for stability, and demonstrating the precompactness of the approximate solutions.
This paper establishes the Limiting Absorption Principle for time-harmonic acoustic and electromagnetic scattering from bi-periodic inhomogeneous layers supporting Bound States in the Continuum, thereby deriving a sharp radiation condition that ensures solution uniqueness by combining the classical Rayleigh expansion with a newly proven orthogonal identity.
This paper demonstrates that a suitable multiplicative Stratonovich noise perturbation can restore well-posedness to the Cauchy problem of a weakly hyperbolic operator with double involutive characteristics, whereas its deterministic counterpart is restricted to well-posedness only within Gevrey classes $1 \leq s < 2$.
This paper establishes the boundary stabilization of flows in star-shaped and tree-shaped open channel networks governed by Saint-Venant equations with friction by constructing a novel explicit Lyapunov function that enables optimal control using only terminal node actuators, even in the absence of internal controls.
This paper establishes the dispersive estimate with a decay rate of for the one-dimensional Schrödinger equation perturbed by a short-range array of delta potentials, provided the coupling constants decay sufficiently and no zero-energy resonance exists.
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.
This paper establishes global Besov regularity estimates for weak solutions to the Dirichlet problem of a fractional -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 and the exponent in both superquadratic and subquadratic regimes.
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.
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.
This paper establishes the existence of a mountain pass solution and proves its global integrability and local Hölder continuity for an entire Choquard equation involving the Grushin operator on .
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.
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.
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.
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.
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.
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.
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.
This paper establishes that mild solutions to the incompressible Navier-Stokes equations with initial data in are weak*-continuous in time and that global solutions vanish in as time approaches infinity.
This paper defines a fractional Ito stochastic integral with respect to a randomly scaled fractional Brownian motion using an -transform approach, establishes the corresponding Ito formula, and applies it to investigate generalized time-fractional evolution equations.
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.