Dynamics of one-fold symmetric patches for the aggregation equation and collapse to singular measure
DOI10.2140/apde.2019.12.2003zbMath1433.35422arXiv1803.07499OpenAlexW2982248385WikidataQ126976048 ScholiaQ126976048MaRDI QIDQ2279787
Publication date: 13 December 2019
Published in: Analysis \& PDE (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1803.07499
Asymptotic behavior of solutions to PDEs (35B40) Vortex flows for incompressible inviscid fluids (76B47) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Population dynamics (general) (92D25) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Blow-up in context of PDEs (35B44) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)
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Cites Work
- Unnamed Item
- Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations
- Contractions in the 2-Wasserstein length space and thermalization of granular media
- An integro-differential equation arising as a limit of individual cell-based models
- Initiation of slime mold aggregation viewed as an instability
- Finite-time blow-up of \(L^\infty \)-weak solutions of an aggregation equation
- Refined blowup criteria and nonsymmetric blowup of an aggregation equation
- L'intégrale de Cauchy définit un opératuer borne sur \(L^ 2 \)pour les courbes lipschitziennes
- A non-local model for a swarm
- Modeling the aggregative behavior of ants of the species Polyergus rufescens
- An interacting particle system modelling aggregation behavior: from individuals to populations
- Global regularity for vortex patches
- Evolution of a cusp-type singularity in a vortex patch
- Diagonal defect measures, adhesion dynamics and Euler equation.
- Equilibria of biological aggregations with nonlocal repulsive-attractive interactions
- Finite-time blow-up of solutions of an aggregation equation in \(\mathbb R^n\)
- Global solutions to vortex density equations arising from sup-conductivity
- Formation of clumps and patches in self-aggregation of finite-size particles
- The Regularity of the Boundary of a Multidimensional Aggregation Patch
- AGGREGATION AND SPREADING VIA THE NEWTONIAN POTENTIAL: THE DYNAMICS OF PATCH SOLUTIONS
- A Primer of Swarm Equilibria
- Lp theory for the multidimensional aggregation equation
- Swarm dynamics and equilibria for a nonlocal aggregation model
- On Similarity Solutions to the Multidimensional Aggregation Equation
- Persistance de structures géométriques dans les fluides incompressibles bidimensionnels
- A gradient flow approach to an evolution problem arising in superconductivity
- Blow-up in multidimensional aggregation equations with mildly singular interaction kernels
- Application of a Theorem of M. G. Krein to Singular Integrals
- Existence de Nappes de Tourbillon en Dimension Deux
- Existence of Weak Solutions to Some Vortex Density Models
- Swarming Patterns in a Two-Dimensional Kinematic Model for Biological Groups
- Stability analysis of swarms
- Local and Global Existence for an Aggregation Equation
- High-field limit for the Vlasov-Poisson-Fokker-Planck system.
