Global bifurcation analysis of mean field equations and the Onsager microcanonical description of two-dimensional turbulence
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Publication:1628782
DOI10.1007/s00526-018-1445-4zbMath1417.35109arXiv1609.04139OpenAlexW2963689148WikidataQ128763664 ScholiaQ128763664MaRDI QIDQ1628782
Publication date: 10 December 2018
Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1609.04139
PDEs in connection with fluid mechanics (35Q35) Variational methods applied to problems in fluid mechanics (76M30) Statistical mechanics of liquids (82D15) Bifurcations in context of PDEs (35B32) Semilinear elliptic equations (35J61) PDEs in connection with statistical mechanics (35Q82)
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Cites Work
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- Topological methods for an elliptic equation with exponential nonlinearities
- Generic multiplicity for a scalar field equation on compact surfaces
- A special class of stationary flows for two-dimensional Euler equations: A statistical mechanics description
- Global analysis for a two-dimensional elliptic eigenvalue problem with the exponential nonlinearity
- On steady distributions of self-attracting clusters under friction and fluctuations
- Some continuation and variational methods for positive solutions of nonlinear elliptic eigenvalue problems
- Harnack type inequality: The method of moving planes
- The sub-harmonic bifurcation of Stokes waves
- Elliptic partial differential equations of second order
- On the existence of blowing-up solutions for a mean field equation
- Non-degeneracy, mean field equations and the Onsager theory of 2D turbulence
- A special class of stationary flows for two-dimensional Euler equations: A statistical mechanics description. II
- Note on two theorems in nonequilibrium statistical mechanics
- Existence and uniqueness for mean field equations on multiply connected domains at the critical parameter
- Existence and non existence results for supercritical systems of Liouville-type equations on simply connected domains
- Supercritical mean field equations on convex domains and the Onsager's statistical description of two-dimensional turbulence
- Singular limits in Liouville-type equations
- Finite Morse index solutions of exponential problems
- Some global results for nonlinear eigenvalue problems
- Quasilinear Dirichlet problems driven by positive sources
- On the convexity of a solution of Liouville's equation
- Global Structure of the Solutions of Non-Linear Real Analytic Eigenvalue Problems
- Finite Morse index solutions of supercritical problems
- Uniform estimates and blow–up behavior for solutions of −δ(u)=v(x)euin two dimensions
- Topological degree for a mean field equation on Riemann surfaces
- STABLE AND UNSTABLE EQUILIBRIA OF UNIFORMLY ROTATING SELF-GRAVITATING CYLINDERS
