ON THE WELL-POSEDNESS OF A 2D NONLINEAR AND NONLOCAL SYSTEM ARISING FROM THE DISLOCATION DYNAMICS

DOI10.1142/S0219199713500211zbMath1292.35165arXiv1210.4072OpenAlexW3098501961MaRDI QIDQ5417131

Dong Li, Liutang Xue, Chang Xing Miao

Publication date: 16 May 2014

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.4072

zbMATH Keywords

dissipationdynamics of dislocation densitiesnonlinear transport equationsnonlocal transport equationsnonlocal modulus of continuity

Mathematics Subject Classification ID

Related Items (6)

On a 1D model with nonlocal interactions and mass concentrations: an analytical-numerical approach* ⋮ Longtime well-posedness for the 2D Groma-Balogh model ⋮ Local well-posedness for the chemotaxis-Navier-Stokes equations in Besov spaces ⋮ Convergence and non-convergence of many-particle evolutions with multiple signs ⋮ Atomistic origins of continuum dislocation dynamics ⋮ On the Regularity Issues of a Class of Drift-Diffusion Equations with Nonlocal Diffusion

Cites Work

• Nonlocal maximum principles for active scalars
• Eventual regularity of the solutions to the supercritical dissipative quasi-geostrophic equation
• On the regularity of a class of generalized quasi-geostrophic equations
• Short time existence and uniqueness in Hölder spaces for the 2D dynamics of dislocation densities
• Global well-posedness for the critical 2D dissipative quasi-geostrophic equation
• Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation
• Global existence for a system of nonlinear and non-local transport equations describing the dynamics of dislocation densities
• A maximum principle applied to quasi-geostrophic equations
• Nonlinear maximum principles for dissipative linear nonlocal operators and applications
• Global solutions of the super-critical 2D quasi-geostrophic equation in Besov spaces
• A new Bernstein's inequality and the 2D dissipative quasi-geostrophic equation
• Dislocation dynamics: Short-time existence and uniqueness of the solution
• Fractal first-order partial differential equations
• The maximum principle and the global attractor for the dissipative 2D quasi-geostrophic equations
• Global Existence Results and Uniqueness for Dislocation Equations
• On the Global Well-Posedness of the Critical Quasi-Geostrophic Equation
• Formation of strong fronts in the 2-D quasigeostrophic thermal active scalar
• Behavior of Solutions of 2D Quasi-Geostrophic Equations
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