On Kato-Ponce and fractional Leibniz

DOI10.4171/rmi/1049zbMath1412.35261arXiv1609.01780OpenAlexW3102415465WikidataQ122897587 ScholiaQ122897587MaRDI QIDQ1733571

Dong Li

Publication date: 21 March 2019

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.01780

zbMATH Keywords

fractional Leibniz Kato-Ponce

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Navier-Stokes equations (35Q30) Fractional partial differential equations (35R11) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23)

Related Items

A simple proof of the generalized Leibniz rule on bounded Euclidean domains ⋮ On some regularity properties for the dispersive generalized Benjamin-Ono-Zakharov-Kuznetsov equation ⋮ Weighted endpoint fractional Leibniz rule ⋮ On the global existence for the compressible Euler-Riesz system ⋮ On the blow up of a non-local transport equation in compact manifolds ⋮ Regular attractor of the β-evolution equation with fractional damping on Rn ⋮ Well-posedness for mean-field evolutions arising in superconductivity ⋮ Local-in-time existence of a free-surface 3D Euler flow with H ^2+δ initial vorticity in a neighborhood of the free boundary ⋮ A first-order Fourier integrator for the nonlinear Schrödinger equation on 𝕋 without loss of regularity ⋮ Embedded exponential-type low-regularity integrators for KdV equation under rough data ⋮ Non existence and strong ill-posedness in $C^k$ and Sobolev spaces for SQG ⋮ Well-posedness for a two-dimensional dispersive model arising from capillary-gravity flows ⋮ On the propagation of regularity for solutions of the dispersion generalized Benjamin-Ono equation ⋮ An Embedded Exponential-Type Low-Regularity Integrator for mKdV Equation ⋮ Global existence and decay rates of solutions to the viscous water-waves system ⋮ On special regularity properties of solutions of the Benjamin-Ono-Zakharov-Kuznetsov (BO-ZK) equation ⋮ Improved blow up criterion for the three dimensional incompressible magnetohydrodynamics system ⋮ Large global solutions for nonlinear Schrödinger equations. II: Mass-supercritical, energy-subcritical cases ⋮ Global solutions of a surface quasigeostrophic front equation ⋮ Paralinearization of the Muskat equation and application to the Cauchy problem ⋮ A short proof of commutator estimates ⋮ Optimal small data scattering for the generalized derivative nonlinear Schrödinger equations ⋮ Size of data in implicit function problems and singular perturbations for nonlinear Schrödinger systems ⋮ Trilinear embedding for divergence-form operators with complex coefficients ⋮ Logarithmically improved extension criteria involving the pressure for the Navier–Stokes equations in Rn$\mathbb {R}^{n}$ ⋮ A semi-discrete first-order low regularity exponential integrator for the ``good Boussinesq equation without loss of regularity ⋮ The IVP for a higher dimensional version of the Benjamin-Ono equation in weighted Sobolev spaces ⋮ Global regularity for a 2D tropical climate model with fractional dissipation ⋮ Nonlinear interaction of three impulsive gravitational waves. II: The wave estimates ⋮ Fractional Leibniz-type rules on spaces of homogeneous type ⋮ Sobolev algebras on Lie groups and noncommutative geometry ⋮ Global well-posedness for the 2D Euler-Boussinesq-Bénard equations with critical dissipation ⋮ Fractional Edgeworth expansions for one-dimensional heavy-tailed random variables and applications ⋮ Global well-posedness and asymptotic behavior in critical spaces for the compressible Euler system with velocity alignment ⋮ Interface Propagation Properties for a Nonlocal Thin-Film Equation ⋮ Spatial decay properties for a model in shear flows posed on the cylinder ⋮ Pointwise decay of solutions to the energy critical nonlinear Schrödinger equations ⋮ Vlasov-Poisson equation in $H^{s, p}(w)$ space ⋮ Relaxation approximation and asymptotic stability of stratified solutions to the IPM equation ⋮ The Cauchy problem for dissipative Benjamin-Ono equation in weighted Sobolev spaces ⋮ Rough bilinear hypersingular integrals ⋮ On the propagation of regularity for solutions of the fractional Korteweg-de Vries equation ⋮ Persistence properties for the dispersion generalized BO-ZK equation in weighted anisotropic Sobolev spaces ⋮ Low regularity well-posedness for the 3D viscous non-resistive MHD system with internal surface wave ⋮ Strong ill-posedness of logarithmically regularized 2D Euler equations in the borderline Sobolev space ⋮ Large global solutions for nonlinear Schrödinger equations. I: Mass-subcritical cases ⋮ Asymptotic behavior for nonlinear Schrödinger equations with critical time-decaying harmonic potential ⋮ Local well-posedness and small data scattering for energy super-critical nonlinear wave equations ⋮ A fully discrete low-regularity integrator for the 1D periodic cubic nonlinear Schrödinger equation ⋮ Sharp commutator estimates via harmonic extensions ⋮ On the Constantin-Lax-Majda model with convection ⋮ Global regularity for a 1D Euler-alignment system with misalignment ⋮ Local well-posedness for fourth order Benjamin-Ono type equations ⋮ Remarks on a nonlocal transport ⋮ Galilean boost and non-uniform continuity for incompressible Euler ⋮ Angled crested like water waves with surface tension: wellposedness of the problem ⋮ Singular support of the global attractor for a damped BBM equation ⋮ On the critical blow up criterion with one velocity component for 3D incompressible MHD system ⋮ Global well-posedness of the 3D generalized Navier-Stokes equations with fractional partial dissipation ⋮ Weighted Leibniz-type rules for bilinear flag multipliers ⋮ Leibniz-type rules for bilinear and biparameter Fourier multiplier operators with applications ⋮ A priori Estimates for the Incompressible Free-Boundary Magnetohydrodynamics Equations with Surface Tension ⋮ On the global existence for the compressible Euler-Poisson system, and the instability of static solutions ⋮ Leibniz-type rules for bilinear Fourier multiplier operators with Besov regularity ⋮ A regularity upgrade of pressure ⋮ Local regularity of weak solutions of the hypodissipative Navier-Stokes equations ⋮ The Kato-Ponce inequality with polynomial weights ⋮ On persistence properties in weighted spaces for solutions of the fractional Korteweg–de Vries equation ⋮ Asymptotics of the three-dimensional Vlasov equation in the large magnetic field limit ⋮ Vlasov-Poisson equation in Besov space ⋮ Global well-posedness to the two-dimensional incompressible vorticity equation in the half plane ⋮ Spectral Convergence of Diffusion Maps: Improved Error Bounds and an Alternative Normalization ⋮ A General Framework of Low Regularity Integrators ⋮ Global regularity results for the 2D Boussinesq equations and micropolar equations with partial dissipation ⋮ Decay rates of solutions to the surface growth equation and the Navier-Stokes system ⋮ The global existence issue for the compressible Euler system with Poisson or Helmholtz couplings ⋮ On the local and global existence of unique solutions to the Lüst model ⋮ Non-decaying solutions to the critical surface quasi-geostrophic equations with symmetries ⋮ Uniform regularity for the nonisentropic MHD system ⋮ On Moffatt's magnetic relaxation equations ⋮ The multilinear Hörmander multiplier theorem with a Lorentz-Sobolev condition

Cites Work

This page was built for publication: On Kato-Ponce and fractional Leibniz