clopen.solutions

Open problems

980 registered problems.

OP-00617 Open
Does a bounded interface slope prevent two-phase Muskat singularities?
AP · AIM Open Applied Problems · free boundaries · Muskat problem · porous media
OP-00618 Open
Global regularity of the three-dimensional Navier–Stokes equations
AP · AIM Open Applied Problems · global regularity · incompressible flows · Navier–Stokes equations
OP-00619 Open
Attainment of the three-dimensional neo-Hookean energy in the regular admissible class
AP · AIM Open Applied Problems · existence of minimizers · neo-Hookean materials · nonlinear elasticity
OP-00620 Open
The no-slip inviscid limit in two dimensions
AP · AIM Open Applied Problems · boundary layers · inviscid limits · Navier–Stokes equations
OP-00621 Open
Large-data global regularity for creeping-flow Oldroyd–B without stress diffusion
AP · AIM Open Applied Problems · global regularity · Oldroyd-B fluids · viscoelastic fluids
OP-00622 Open
Vanishing nonlinear viscosity without commuting transport and diffusion matrices
AP · AIM Open Applied Problems · BV solutions · hyperbolic conservation laws · vanishing viscosity
OP-00623 Open
Automatic conservation laws for renormalized nonlinear diffusion
AP · AIM Open Applied Problems · conservation laws · reaction–diffusion systems · renormalized solutions
OP-00624 Open
Optimal nonlocal obstacle regularity with a minimally smooth obstacle
AP · AIM Open Applied Problems · integro-differential operators · obstacle problems · optimal stopping
OP-00625 Open
Soliton resolution for bounded nonradial energy-critical waves
AP · AIM Open Applied Problems · energy-critical wave equations · soliton resolution
OP-00626 Open
Global regularity of viscous planar MHD without magnetic diffusion
AP · AIM Open Applied Problems · global regularity · magnetohydrodynamics
OP-00627 Open
Large-data weak solutions for three-dimensional stress-diffusive Oldroyd-B flow
AP · AIM Open Applied Problems · Oldroyd-B model · viscoelastic fluids · weak solutions
OP-00628 Open
Axisymmetry of equilibrium distributions for Onsager rods
AP · AIM Open Applied Problems · nematic liquid crystals · Onsager model
OP-00629 Open
Finiteness of interior defects in Oseen–Frank minimizers
AP · AIM Open Applied Problems · nematic liquid crystals · Oseen–Frank energy · point defects
OP-00630 Open
Strong comparison for ordered p-harmonic fields
AP · AIM Open Applied Problems · comparison principles · p-harmonic functions
OP-00631 Open
Finite-time growth of total variation in physical gas dynamics
AP · AIM Open Applied Problems · entropy solutions · hyperbolic conservation laws
OP-00632 Open
Asymptotic stability of the phi-four kink without odd symmetry
AP · AIM Open Applied Problems · asymptotic stability · kinks · scalar field equations
OP-00633 Open
Finite-time collapse in the planar self-steepening Schrödinger equation
AP · AIM Open Applied Problems · derivative nonlinear Schrödinger equations · finite-time blow-up
OP-00634 Open
Existence of elastic equilibria under quasiconvexity and infinite compression energy
AP · AIM Open Applied Problems · calculus of variations · nonlinear elasticity · quasiconvexity
OP-00635 Open
The densest packing of congruent regular tetrahedra
MG · AIM Open Applied Problems · packing densities · regular tetrahedra
OP-00636 Open
Global classical solutions for repulsive relativistic Vlasov–Poisson
AP · AIM Open Applied Problems · collisionless plasmas · Vlasov–Poisson systems
OP-00637 Open
Global classical continuation for a reversible mass-action reaction
AP · AIM Open Applied Problems · mass-action kinetics · reaction–diffusion systems
OP-00638 Open
Bounded variation of gradients in the Rudin–Osher–Fatemi denoising model
AP · AIM Open Applied Problems · functions of bounded variation · total variation minimizers
OP-00639 Open
Hölder regularity under directional nonlocal ellipticity alone
AP · AIM Open Applied Problems · Hölder estimates · integro-differential equations · jump processes
OP-00640 Open
Global smoothness for the real scalar defocusing septic wave equation
AP · AIM Open Applied Problems · energy-supercritical equations · finite-time blow-up · nonlinear wave equations
OP-00641 Open
Global smooth Schrödinger maps below the degree-zero energy threshold
AP · AIM Open Applied Problems · energy-critical dispersive equations · Landau–Lifshitz equation · Schrödinger maps
OP-00642 Open
Sharp gradient regularity for higher-dimensional p-Poisson equations
AP · AIM Open Applied Problems · gradient regularity · p-Laplace equations
OP-00643 Open
Nonlinear orbital stability of small solitary gravity waves
AP · AIM Open Applied Problems · orbital stability · solitary waves · water waves
OP-00644 Open
The quadruple-bubble conjecture in three-dimensional space
DG · AIM Open Applied Problems · isoperimetric clusters · soap bubbles
OP-00645 Open
Optimal dimension for bounded subquadratic p-Laplace extremal states
AP · AIM Open Applied Problems · extremal solutions · p-Laplace equations
OP-00646 Open
Global regularity for supercritical dissipative surface quasi-geostrophic flow
AP · AIM Open Applied Problems · fractional dissipation · global regularity · quasi-geostrophic equations
OP-00647 Open
Global smoothness of the one-dimensional surface-growth equation
AP · AIM Open Applied Problems · fourth-order parabolic equations · global regularity · surface growth models
OP-00648 Open
Preservation of strict positivity for the cubic thin-film equation
AP · AIM Open Applied Problems · degenerate parabolic equations · thin-film equations
OP-00649 Open
Barenblatt attraction for porous-medium diffusion with time memory
AP · AIM Open Applied Problems · Caputo derivatives · large-time behaviour · porous medium equations
OP-00650 Open
Uniqueness for a point source in time-fractional porous-medium flow
AP · AIM Open Applied Problems · Caputo derivatives · fundamental solutions · porous medium equations
OP-00651 Open
Largest radius ratio in nonuniform triangulated circle packings
MG · AIM Open Applied Problems · circle packings · triangulations
OP-00652 Open
Global regularity for two-dimensional Kuramoto–Sivashinsky on arbitrary square tori
AP · AIM Open Applied Problems · global regularity · growing modes · Kuramoto–Sivashinsky equation
OP-00653 Open
The ball as the least densely packable convex solid
MG · AIM Open Applied Problems · convex bodies · Kepler conjecture · packing densities
OP-00654 Open
Self-sustained oscillations in the full voltage–conductance neuron equation
AP · AIM Open Applied Problems · kinetic equations · neural networks · periodic solutions
OP-00655 Open
Finite-time singularity formation for unconstrained Willmore flow
DG · AIM Open Applied Problems · finite-time singularities · geometric flows · Willmore flow
OP-00656 Open
Scattering of arbitrary small energy data for the three-dimensional Zakharov system
AP · AIM Open Applied Problems · dispersive equations · scattering · Zakharov system
OP-00657 Open
Finite-time Langmuir collapse for the three-dimensional Zakharov system
AP · AIM Open Applied Problems · blow-up · Langmuir waves · Zakharov system
OP-00658 Solution claimed
Global optimality of the Abrikosov triangular lattice
AP · Abrikosov lattice · AIM Open Applied Problems · Coulomb gases · renormalized energy
OP-00659 Solution claimed
Absence of doubly infinite minimizing paths in planar first-passage percolation
PR · AIM Open Applied Problems · bigeodesics · first-passage percolation
OP-00660 Solution claimed
Affine Bernstein rigidity in dimensions three through nine
AP · affine maximal hypersurfaces · AIM Open Applied Problems · Bernstein problem · fourth-order elliptic equations
OP-00661 Solution claimed
Can entangled codewords improve amplitude-damping classical capacity?
MP · AIM Open Applied Problems · amplitude damping channel · classical capacity · Holevo information
OP-00662 Solution claimed
Logarithmic controlled bandwidth for locally analytic functions
NA · AIM Open Applied Problems · bandlimited approximation · Levin method · oscillatory integrals
OP-00663 Solution claimed
Extended states in the three-dimensional Anderson model
SP · absolutely continuous spectrum · AIM Open Applied Problems · Anderson model · random Schrödinger operators
OP-00664 Solution claimed
Calderón uniqueness from an arbitrary local boundary patch
AP · AIM Open Applied Problems · Calderón problem · inverse conductivity problem · partial data
OP-00665 Solution claimed
Smooth approximation of three-dimensional Sobolev homeomorphisms
FA · AIM Open Applied Problems · diffeomorphic approximation · nonlinear elasticity · Sobolev homeomorphisms
OP-00666 Solution claimed
Global Birkhoff billiard integrability conjecture
DS · AIM Open Applied Problems · Birkhoff conjecture · caustics · convex billiards