Regularity of solutions of the fractional porous medium flow with exponent $1/2$
From MaRDI portal
Publication:2797731
DOI10.1090/spmj/1397zbMath1335.35273arXiv1409.8190OpenAlexW2964249730MaRDI QIDQ2797731
Luis A. Caffarelli, Juan Luis Vazquez
Publication date: 6 April 2016
Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1409.8190
degenerate parabolic equationporous medium equationHölder regularityfractional Laplaciannonlocal diffusion operator
Nonlinear parabolic equations (35K55) Flows in porous media; filtration; seepage (76S05) Degenerate parabolic equations (35K65) Fractional partial differential equations (35R11)
Related Items (19)
The Dirichlet problem for the fractional \(p\)-Laplacian evolution equation ⋮ The flow of polynomial roots under differentiation ⋮ Global Regularity for a Nonlocal PDE Describing Evolution of Polynomial Roots Under Differentiation ⋮ Finite and infinite speed of propagation for porous medium equations with nonlocal pressure ⋮ Gradient flows of modified Wasserstein distances and porous medium equations with nonlocal pressure ⋮ Global solutions to the tangential Peskin problem in 2-D ⋮ Global solutions of aggregation equations and other flows with random diffusion ⋮ A gradient flow approach to the porous medium equation with fractional pressure ⋮ Complexity of asymptotic behavior of solutions for the fractional porous medium equation ⋮ From the Peierls-Nabarro model to the equation of motion of the dislocation continuum ⋮ Exact controllability of fractional order evolution equations in Banach spaces ⋮ Hyers-Ulam stability of a nonautonomous semilinear equation with fractional diffusion ⋮ Porous medium equation with nonlocal pressure in a bounded domain ⋮ Singularity formation for the fractional Euler-alignment system in 1D ⋮ Existence of weak solutions for a general porous medium equation with nonlocal pressure ⋮ Longtime behavior and weak-strong uniqueness for a nonlocal porous media equation ⋮ Liouville theorem involving the uniformly nonlocal operator ⋮ Non-local porous media equations with fractional time derivative ⋮ Existence of weak solutions to a continuity equation with space time nonlocal Darcy law
Cites Work
- Regularity of solutions of the fractional porous medium flow
- A mass-transportation approach to a one dimensional fluid mechanics model with nonlocal velocity
- Finite time singularities in a 1D model of the quasi-geostrophic equation
- A fractional porous medium equation
- Nonlinear diffusion of dislocation density and self-similar solutions
- Nonlinear porous medium flow with fractional potential pressure
- Global existence, singularities and ill-posedness for a nonlocal flux
- Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation
- Analytic structure of two 1D-transport equations with nonlocal fluxes
- Asymptotic behaviour of a porous medium equation with fractional diffusion
- Recent progress in the theory of nonlinear diffusion with fractional Laplacian operators
- A mean field equation as limit of nonlinear diffusions with fractional Laplacian operators
- Barenblatt solutions and asymptotic behaviour for a nonlinear fractional heat equation of porous medium type
- From the long jump random walk to the fractional Laplacian
- A General Fractional Porous Medium Equation
- Nonlinear Diffusion with Fractional Laplacian Operators
- Regularity theory for parabolic nonlinear integral operators
- An Extension Problem Related to the Fractional Laplacian
- Unnamed Item
- Unnamed Item
This page was built for publication: Regularity of solutions of the fractional porous medium flow with exponent $1/2$
