On the differentiability issue of the drift-diffusion equation with nonlocal Lévy-type diffusion
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Publication:1683520
DOI10.2140/pjm.2018.293.471zbMath1379.35049arXiv1601.03123OpenAlexW3103269923MaRDI QIDQ1683520
Publication date: 1 December 2017
Published in: Pacific Journal of Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1601.03123
Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) A priori estimates in context of PDEs (35B45) Fractional partial differential equations (35R11) Integro-partial differential equations (35R09)
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Cites Work
- Unnamed Item
- The 2D Boussinesq equations with logarithmically supercritical velocities
- Fractional operators with singular drift: smoothing properties and Morrey-Campanato spaces
- A frequency localized maximum principle applied to the 2D quasi-geostrophic equation
- Regularity results for nonlocal equations by approximation
- Global well-posedness for the critical 2D dissipative quasi-geostrophic equation
- A priori estimates for integro-differential operators with measurable kernels
- Regularity of Hölder continuous solutions of the supercritical quasi-geostrophic equation
- Global regularity for a logarithmically supercritical hyperdissipative Navier-Stokes equation
- Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation
- Quasi-geostrophic equations, nonlinear Bernstein inequalities and \(\alpha\)-stable processes
- A maximum principle applied to quasi-geostrophic equations
- Uniform estimates for fundamental solutions associated with nonlocal Dirichlet forms
- Nonlinear maximum principles for dissipative linear nonlocal operators and applications
- On the loss of continuity for super-critical drift-diffusion equations
- On a maximum principle and its application to the logarithmically critical Boussinesq system
- A new Bernstein's inequality and the 2D dissipative quasi-geostrophic equation
- On fundamental solutions for non-local parabolic equations with divergence free drift
- Markov chain approximations for symmetric jump processes
- Global well-posedness of slightly supercritical active scalar equations
- Regularity theory for parabolic nonlinear integral operators
- Fourier Analysis and Nonlinear Partial Differential Equations
- Hölder estimates for advection fractional-diffusion equations
- On the differentiability of the solution to an equation with drift and fractional diffusion
- An Extension Problem Related to the Fractional Laplacian
