253 papers
This paper establishes the uniqueness of ground state solutions for the nonlinear Schrödinger equation with an inverse square potential by adapting the classical shooting method, and subsequently utilizes this result alongside spectral analysis to construct stable/unstable manifolds and classify solutions on the mass-energy level surface in dimensions .
This paper establishes a new existence theory for equilibria in continuous-time time-inconsistent stochastic control problems by proving that solutions to entropy-regularized exploratory equilibrium HJB equations converge to a weak solution of the generalized equilibrium HJB equation as the regularization vanishes, thereby resolving the open problem of existence without requiring strong regularity assumptions.
This paper investigates the asymptotic behavior of ground states for the nonlinear Schrödinger equation at endpoint powers, proving strong convergence with explicit bounds to a Gaussian "Gausson" in the logarithmic limit and to an Aubin-Talenti algebraic soliton in dimensions three and higher.
This paper proves that -dimensional solutions to the Einstein scalar-field Vlasov system, initially close to FLRW spacetimes on closed surfaces of arbitrary genus, exhibit stable Big Bang singularities with quiescent, velocity-term-dominated asymptotics and -inextendibility, thereby establishing the Strong Cosmic Censorship conjecture for a corresponding class of polarized -symmetric vacuum solutions.
This paper utilizes Arnold's geometric approach and matrix theory to prove the Lyapunov stability and establish a rigidity condition for steady states in Zeitlin's discretized 2-D Euler model, thereby validating its reliability for studying stationary solutions and highlighting connections between matrix theory and nonlinear PDE techniques.
This paper establishes the local-in-time existence of strong solutions to the gravity water wave kinetic equation by rigorously deriving a sharper bound for the collision kernel's growth in the highly non-local regime and utilizing this improved estimate to overcome the associated singular integral challenges.
This paper introduces a simple condition ensuring the uniqueness of weak, entropy-admissible solutions for scalar conservation laws with discontinuous gradient-dependent flux by proving that such solutions coincide with the contractive semigroup trajectory generated by vanishing viscosity and front tracking approximations.
This paper establishes a conformal lower bound for weighted Dirac eigenvalues on compact spin manifolds with chiral boundary conditions in terms of the relative Yamabe constant, proving that equality is achieved if and only if the manifold is conformally equivalent to a hemisphere supporting a Killing spinor.
This study presents the first explicit reconstruction of a Loewner driving function from the expanding boundaries of a growing slime mold, demonstrating that its growth front exhibits emergent Brownian-like conformal dynamics and establishing a quantitative framework linking morphogenesis to stochastic geometry.
This paper establishes that for the three-dimensional degenerate compressible Navier-Stokes equations with nonlinear viscosity coefficients depending on density, smooth solutions can develop finite-time implosions at the origin provided the viscosity power-law exponent falls below a specific threshold determined by the adiabatic exponent, a result proven through novel pointwise density estimates and weighted high-order energy methods that demonstrate the viscous terms are insufficient to suppress the convective implosion mechanism.
This paper provides a complete local description of the moduli space of dynamical spherically symmetric black hole spacetimes near the Reissner-Nordström family, characterizing the black hole threshold as the extremal leaf of a foliation and establishing universal scaling laws with a critical exponent of $1/2$ alongside the activation of Aretakis instability for threshold solutions.
This study investigates how inertial effects influence autotoxicity-mediated vegetation patterns on sloped arid terrains using a hyperbolic extension of the Klausmeier model, revealing that inertia acts as a destabilizing mechanism that enlarges the parameter range for uphill migrating bands, can induce hysteresis by reversing bifurcation regimes near onset, and increases pulse speeds in far-from-equilibrium conditions.
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 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 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 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 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 the existence, energy decay, and blow-up behavior of solutions for a three-dimensional piezoelectric beam model with nonlinear dampings and supercritical sources by utilizing nonlinear semigroups, the potential well method, and differential inequality techniques, while removing restrictive conditions on model coefficients.
This paper establishes the global well-posedness of the elastic-viscous-plastic (EVP) sea-ice model under inviscid Voigt-regularization, thereby resolving the long-standing issue of handling viscosity coefficients without cutoff that has hindered the analysis of related sea-ice models.
This paper proves a theorem by C. Miranda regarding the Hölder regularity of generalized layer potential convolution operators acting on the boundary of a open set when the densities are of class .