Partial differential equations with quadratic nonlinearities viewed as matrix-valued optimal ballistic transport problems
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Publication:2113550
DOI10.1007/s00205-022-01754-8OpenAlexW3033212531WikidataQ114231138 ScholiaQ114231138MaRDI QIDQ2113550
Publication date: 14 March 2022
Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1905.06059
Smoothness and regularity of solutions to PDEs (35B65) KdV equations (Korteweg-de Vries equations) (35Q53) Variational methods applied to PDEs (35A15) Viscoelastic fluids (76A10) Variational problems in a geometric measure-theoretic setting (49Q20) Magnetohydrodynamics and electrohydrodynamics (76W05) Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20) Weak solutions to PDEs (35D30) Existence, uniqueness, and regularity theory for incompressible inviscid fluids (76B03) Euler equations (35Q31) Optimal transportation (49Q22)
Cites Work
- Unnamed Item
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- Geometry of diffeomorphism groups, complete integrability and geometric statistics
- On Euler's equation and `EPDiff'
- From Vlasov-Poisson to Korteweg-de Vries and Zakharov-Kuznetsov
- Wild solutions for 2D incompressible ideal flow with passive tracer
- Non-uniqueness and \(h\)-principle for Hölder-continuous weak solutions of the Euler equations
- Oscillations and concentrations in weak solutions of the incompressible fluid equations
- Weak-strong uniqueness for measure-valued solutions
- Existence of weak solutions for the incompressible Euler equations
- Global small solutions of 3D incompressible Oldroyd-B model without damping mechanism
- The Camassa-Holm equation as an incompressible Euler equation: a geometric point of view
- On admissibility criteria for weak solutions of the Euler equations
- Optimal mass transportation and Mather theory
- The Euler equations as a differential inclusion
- The Euler-Poincaré equations and semidirect products with applications to continuum theories
- Geometry and curvature of diffeomorphism groups with \(H^1\) metric and mean hydrodynamics
- Topological methods in hydrodynamics
- The geometry and analysis of the averaged Euler equations and a new diffeomorphism group
- A new optimal transport distance on the space of finite Radon measures
- An interpolating distance between optimal transport and Fisher-Rao metrics
- Global well-posedness of the incompressible magnetohydrodynamics
- Analytic results related to magneto-hydrodynamic turbulence
- A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
- The initial value problem for the Euler equations of incompressible fluids viewed as a concave maximization problem
- Loomis-Whitney-type inequalities and low regularity well-posedness of the periodic Zakharov-Kuznetsov equation
- Bounded solutions of ideal MHD with compact support in space-time
- Global well-posedness for the Cauchy problem of the Zakharov-Kuznetsov equation in 2D
- Young measures generated by ideal incompressible fluid flows
- Generalized compressible flows and solutions of the \(H(\text{div})\) geodesic problem
- Embedding Camassa-Holm equations in incompressible Euler
- On the ideal magnetohydrodynamics in three-dimensional thin domains: well-posedness and asymptotics
- Uniformly compressing mean curvature flow
- Uniform bound of the highest energy for the three dimensional incompressible elastodynamics
- Generalized Hunter-Saxton equations, optimal information transport, and factorization of diffeomorphisms
- Optimal transport for applied mathematicians. Calculus of variations, PDEs, and modeling
- Riemannian geometries on spaces of plane curves
- Sur la géométrie différentielle des groupes de Lie de dimension infinite et ses applications à l'hydrodynamique des fluides parfaits
- Groups of diffeomorphisms and the motion of an incompressible fluid
- Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms
- Optimal Transport in Competition with Reaction: The Hellinger--Kantorovich Distance and Geodesic Curves
- Global Well-Posedness of Incompressible Elastodynamics in Two Dimensions
- The Cauchy Problem for the Euler–Poisson System and Derivation of the Zakharov–Kuznetsov Equation
- Almost Local Metrics on Shape Space of Hypersurfaces inn-Space
- Almost global existence for 2-D incompressible isotropic elastodynamics
- Hidden convexity in some nonlinear PDEs from geometry and physics
- Global generalized solutions for Maxwell-alpha and Euler-alpha equations
- Global Regularity for Some Oldroyd‐B Type Models
- Global Solutions of Two-Dimensional Incompressible Viscoelastic Flows with Discontinuous Initial Data
- Longtime Dynamics of a Conductive Fluid in the Presence of a Strong Magnetic Field
- The Least Action Principle and the Related Concept of Generalized Flows for Incompressible Perfect Fluids
- Topological Approximation Methods for Evolutionary Problems of Nonlinear Hydrodynamics
- The Geometry of Infinite-Dimensional Groups
- On the formulation of rheological equations of state
- Polar factorization and monotone rearrangement of vector‐valued functions
- Relaxation of the incompressible porous media equation
- Global existence for three‐dimensional incompressible isotropic elastodynamics via the incompressible limit
- Fluid Mechanics
- Sharp global well-posedness for KdV and modified KdV on ℝ and 𝕋
- On Optimal Transport of Matrix-Valued Measures
- Dynamic and stochastic propagation of the Brenier optimal mass transport
- Information Geometry
- Global existence for three‐dimensional incompressible isotropic elastodynamics
- The Definition of a Quadratic Form
- On hydrodynamics of viscoelastic fluids
- Optimal Transport
- Shapes and diffeomorphisms
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