A short note on maximal regularity for the heat kernel in Besov spaces and a degenerate 3D Keller-Segel system
We prove global existence for a degenerate Keller-Segel equation with small initial values in a critical Lorentz space.
math.AP↗
arXiv subjects
Pierre Gilles Lemarié-Rieusset
Publications and source records attributed to Pierre Gilles Lemarié-Rieusset.
Calder{ó}n splitting and weak solutions for Navier-Stokes equations with initial data in weighted L p spaces
We show the existence of global weak solutions of the 3D Navier-Stokes equations with initial velocity in the weighted spaces , using Calder{ó}n splitting L p $Φ$$γ$ $\subset$ L 2 $Φ$ 2 + L r (with some r $\in$ (3, +$\infty$)) and energy controls in L 2 $Φ$ 2 .
math.AP↗
Highly singular (frequentially sparse) steady solutions for the 2D Navier-Stokes equations on the torus
We construct non-trivial steady solutions in $H^{-1}$ for the 2D Navier-Stokes equations on the torus. In particular, the solutions are not square integrable, so that we have to redefine the notion of solutions.
math.AP↗
The Navier-Stokes equations in mixed-norm time-space parabolic Morrey spaces
We discuss the Navier-Stokes equations with forces in the mixed norm time-space parabolic Morrey spaces of Krylov.
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A remark on weak-strong uniqueness for suitable weak solutions of the Navier-Stokes equations
We extend Barker's weak-strong uniqueness results for the Navier--Stokes equations and consider a criterion involving Besov spaces and weighted Lebesgue spaces.
math.AP↗
Weighted energy estimates for the incompressible Navier-Stokes equations and applications to axisymmetric solutions without swirl
We consider a family of weights which permit to generalize the Leray procedure to obtain weak suitable solutions of the 3D incom-pressible Navier-Stokes equations with initial data in weighted L 2 spaces. Our principal result concerns the existence of regular global solutions when the initial velocity is an axisymmetric vector field without swirl such that both the initial velocity and its vorticity belong to L 2 ((1 + r 2) -- $γ$ 2 dx), with r = x 2 1 + x 2 2 and $γ$ $\in$ (0, 2).
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Characterisation of the pressure term in the incompressible Navier-Stokes equations on the whole space
We characterise the pressure term in the incompressible 2D and 3D Navier-Stokes equations for solutions defined on the whole space.
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Real variable methods in harmonic analysis and Navier-Stokes equations
Real variable methods in harmonic analysis were developed throughout the works of E.M. Stein. They turn out to be a powerful tool for the study of non-linear PDEs. We illustrate this point by discussing various points of the modern theory of Navier-Stokes equations.
math.AP↗
Weak solutions for Navier--Stokes equations with initial data in weighted $L^2$ spaces
We show the existence of global weak solutions of the 3D Navier-Stokes equations with initial velocity in the weighted spaces L 2 w$γ$ , where w $γ$ (x) = (1 + |x|) --$γ$ and 0 < $γ$ $\le$ 2, using new energy controls. As application we give a new proof of the existence of global weak discretely self-similar solutions of the 3D Navier-Stokes equations for discretely self-similar initial velocities which are locally square inte-grable.
math.AP↗
Interpolation, extrapolation, Morrey spaces and local energy control for the Navier--Stokes equations
Barker recently proved new weak-strong uniqueness results for the Navier-Stokes equations based on a criterion involving Besov spaces and a proof through interpolation between Besov-H{ö}lder spaces and L 2. We improve slightly his results by considering Besov-Morrey spaces and interpolation between Besov-Morrey spaces and L 2 uloc. Let u 0 a divergence-free vector field on R 3. We shall consider weak solutions to the Cauchy initial value problem for the Navier-Stokes equations which satisfy energy estimates. The differential Navier-Stokes equations read as $\partial$ t u + u. $\nabla$ u = $Δ$ u -- $\nabla$p div u = 0 u(0, .) = u 0 *
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Frequency decay for Navier-Stokes stationary solutions
We consider stationary Navier-Stokes equations in R 3 with a regular external force and we prove exponential frequency decay of the solutions. Moreover, if the external force is small enough, we give a pointwise exponential frequency decay for such solutions according to the K41 theory. If a damping term is added to the equation, a pointwise decay is obtained without the smallness condition over the force.
math.AP↗
Local stability of energy estimates for the Navier--Stokes equations
We study the regularity of the weak limit of a sequence of dissipative solutions to the Navier--Stokes equations when no assumptions is made on the behavior of the pressures.
math.AP↗