OOIR: Observatory of International Research

Papers

(The median citation count of Communications in Partial Differential Equations is 1. The table below lists those papers that are above that threshold based on CrossRef citation counts [max. 250 papers]. The publications cover those that have been published in the past four years, i.e., from 2021-05-01 to 2025-05-01.)

Article	Citations
New asymptotics for strong solutions of the strongly stratified Boussinesq system without rotation and for large ill-prepared initial data	83
Slow periodic homogenization for Hamilton–jacobi equations	20
Logarithmic Gross-Pitaevskii equation	17
Uniform convergence rates and Lipschitz regularity estimates in periodic homogenization of high-contrast elliptic systems	17
On solutions to −Δ u = Vu near infinity	16
Low regularity well-posedness for two-dimensional deep gravity water waves with constant vorticity	14
Nodal sets for broken quasilinear partial differential equations with Dini coefficients	13
Initial data identification in space dependent conservation laws and Hamilton-Jacobi equations	12
Taxis-driven persistent localization in a degenerate Keller-Segel system	11
Dirichlet problem for weakly harmonic maps with rough data	11
On the vanishing discount approximation for compactly supported perturbations of periodic Hamiltonians: the 1d case	11
Asymptotic stability of solutions to the Navier–Stokes–Fourier system driven by inhomogeneous Dirichlet boundary conditions	10
Erratum to “optimal relaxation of bump-like solutions of the one-dimensional Cahn–Hilliard equation”	10
Segregated solutions for nonlinear Schrödinger systems with weak interspecies forces	10
Analysis of the generalized Aw-Rascle model	9
The Pauli-Poisson equation and its semiclassical limit	9
The streamlines of ∞-harmonic functions obey the inverse mean curvature flow	8
Optimal relaxation of bump-like solutions of the one-dimensional Cahn–Hilliard equation	8
A minimization procedure to the existence of segregated solutions to parabolic reaction-diffusion systems	8
Sticky particle Cucker–Smale dynamics and the entropic selection principle for the 1D Euler-alignment system	7
Stochastic homogenization of nonconvex viscous Hamilton-Jacobi equations in one space dimension	7
Existence of weak solutions to multiphase Cahn–Hilliard–Darcy and Cahn–Hilliard–Brinkman models for stratified tumor growth with chemotaxis and general source terms	7
Some applications of heat flow to Laplace eigenfunctions	6
Asymptotic estimates for the wave functions of the Dirac-Coulomb operator and applications	6
Existence of martingale solutions to a nonlinearly coupled stochastic fluid-structure interaction problem	6

Maximal speed of quantum propagation for the Hartree equation	6
Carleman estimates and boundedness of associated multiplier operators	6
Quantitative mixing and dissipation enhancement property of Ornstein–Uhlenbeck flow	6
Stationary equilibria and their stability in a Kuramoto MFG with strong interaction	6
Scaling asymptotics of Wigner distributions of harmonic oscillator orbital coherent states	6
Inhomogeneous global minimizers to the one-phase free boundary problem	6
New Lipschitz estimates and long-time asymptotic behavior for porous medium and fast diffusion equations	6
On smoothness and uniqueness of multi-solitons of the non-linear Schrödinger equations	5
Homogenization of some periodic Hamilton-Jacobi equations with defects	5
Nonlocal-to-local convergence rates for strong solutions to a Navier-Stokes-Cahn-Hilliard system with singular potential	5
Quasilinear wave equations on Schwarzschild–de Sitter	5
Nonlinear enhanced dissipation in viscous Burgers type equations II	5
Quantitative Hardy inequalities for magnetic Hamiltonians	4
The Dirichlet-to-Neumann map for a semilinear wave equation on Lorentzian manifolds	4
Measure-valued solutions to the stochastic compressible Euler equations and incompressible limits	4
On the Cauchy problem for the Muskat equation with non-Lipschitz initial data	4
Quantum entanglement and the growth of Laplacian eigenfunctions	4
Sharp convergence rates for Darcy’s law	4
A weakly turbulent solution to the cubic nonlinear harmonic oscillator on ℝ ² perturbed by a real smooth potential decaying to zero at infinity	4
Dimension reduction techniques in deterministic mean field games	4
Polynomial convergence rate for quasi-periodic homogenization of Hamilton-Jacobi equations and application to ergodic estimates	4
Construction of high regularity invariant measures for the 2D Euler equations and remarks on the growth of the solutions	4
Strichartz estimates for Maxwell equations in media: the partially anisotropic case	4
L²-type Lyapunov functions for hyperbolic scalar conservation laws	4
About the wave equation outside two strictly convex obstacles	4
Horizontal magnetic fields and improved Hardy inequalities in the Heisenberg group	4
A superposition principle for the inhomogeneous continuity equation with Hellinger–Kantorovich-regular coefficients	4
A Globally Stable Self-Similar Blowup Profile in Energy Supercritical Yang-Mills Theory	3
Global existence for the two-dimensional Kuramoto-Sivashinsky equation with advection	3
Steady solutions for the Schrödinger map equation	3
Phenotypic heterogeneity in a model of tumour growth: existence of solutions and incompressible limit	3
Non-Newtonian two-phase thin-film problem: Local existence, uniqueness, and stability	3
A PDE framework of consensus-based optimization for objectives with multiple global minimizers	3
Remarks on local regularity of axisymmetric solutions to the 3D Navier–Stokes equations	3
Small data global regularity for half-wave maps in n = 4 dimensions	3
Lotka–Volterra competition-diffusion system: the critical competition case	3
Nondispersive solutions to the mass critical half-wave equation in two dimensions	3
Sharp conditions for scattering and blow-up for a system of NLS arising in optical materials with χ³ nonlinear response	3
Spectral asymptotics for the vectorial damped wave equation	3
A microscopic derivation of Gibbs measures for the 1D focusing cubic nonlinear Schrödinger equation	3
Periodic solutions to integro-differential equations: variational formulation, symmetry, and regularity	3
Condenser capacities and capacitary potentials for unbounded sets, and global p -harmonic Green functions on metric spaces	2
On the limiting amplitude principle for the wave equation with variable coefficients	2
Spectral theory for Maxwell’s equations at the interface of a metamaterial. Part II: Limiting absorption, limiting amplitude principles and interface resonance	2
On the growth of generalized Fourier coefficients of restricted eigenfunctions	2
Shape optimization for nonlocal anisotropic energies	2
Spontaneous curvature effects of the Helfrich flow: singularities and convergence	2
Monotone solutions for mean field games master equations: continuous state space and common noise	2
Boundary renormalisation of SPDEs	2
Well-posedness of Hamilton-Jacobi equations in the Wasserstein space: non-convex Hamiltonians and common noise	2

A Hamilton-Jacobi approach to evolution of dispersal	2
Periodic homogenization for weakly elliptic Hamilton-Jacobi-Bellman equations with critical fractional diffusion	2
The Hele–Shaw flow as the sharp interface limit of the Cahn–Hilliard equation with disparate mobilities	2
Convergence towards equilibrium for a model with partial diffusion	2
Propagation of chaos for the Cucker-Smale systems under heavy tail communication	2
Threshold scattering for the 2D radial cubic-quintic NLS	2
Dirichlet problems in perforated domains	2
From resolvent expansions at zero to long time wave expansions	2
Existence of a weak solution to a nonlinear fluid-structure interaction problem with heat exchange	2
Boundary Lebesgue mixed-norm estimates for non-stationary Stokes systems with VMO coefficients	2
Cost of observability inequalities for elliptic equations in 2-d with potentials and applications to control theory	2
Partial regularity of the heat flow of half-harmonic maps and applications to harmonic maps with free boundary	1
Potential flows away from stagnation in infinite cylinders	1
Selection by vanishing common noise for potential finite state mean field games	1
Topological invariants for interface modes	1
Asymptotics and scattering for wave Klein-Gordon systems	1
Global well-posedness for the Vlasov-Poisson system with massless electrons in the 3-dimensional torus	1
Reversed Strichartz estimates for wave on non-trapping asymptotically hyperbolic manifolds and applications	1
A fractional Hopf Lemma for sign-changing solutions	1
The Yang-Mills heat flow with random distributional initial data	1
Hexagonal structures in 2D Navier–Stokes flows	1
The Poisson equation involving surface measures	1
The convergence rate of p -harmonic to infinity-harmonic functions	1
The Willmore flow with prescribed isoperimetric ratio	1
Dissipation enhancing properties for a class of Hamiltonian flows with closed streamlines	1
Threshold solutions for the 3 d cubic-quintic NLS	1
The lifespan of small data solutions for intermediate long wave equation (ILW)	1
Stable discontinuous stationary solutions to reaction-diffusion-ODE systems	1
Green’s function of heat equation for heterogeneous media in 3-D	1
A variational approach to first order kinetic mean field games with local couplings	1
Topological Anderson insulators by homogenization theory	1
On a generalized Aviles-Giga functional: compactness, zero-energy states, regularity estimates and energy bounds	1
Stability estimates for the holonomy inverse problem	1
Global existence, uniform boundedness, and stabilization in a chemotaxis system with density-suppressed motility and nutrient consumption	1
Duality solutions to the hard-congestion model for the dissipative Aw-Rascle system	1
Dissipative structure for symmetric hyperbolic-parabolic systems with Korteweg-type dispersion	1
Propagation of velocity moments and uniqueness for the magnetized Vlasov–Poisson system	1
On the motion of a small rigid body in a viscous compressible fluid	1
Transport of Gaussian measures under the flow of one-dimensional fractional nonlinear Schrödinger equations	1
Mean field limit for congestion dynamics	1
Doubling inequalities and nodal sets in periodic elliptic homogenization	1