Well-posedness and regularity for a polyconvex energy
DOI10.1051/cocv/2023041zbMath1522.49026arXiv2011.03876OpenAlexW3101171368MaRDI QIDQ6138497
Matthew Jacobs, Inwon Christina Kim, Wilfrid Gangbo
Publication date: 5 September 2023
Published in: ESAIM: Control, Optimisation and Calculus of Variations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2011.03876
regularitywell-posednesscalculus of variationsEkeland variational principleconvex dualitypolyconvexityNavier-Stokes
Sensitivity, stability, well-posedness (49K40) Navier-Stokes equations for incompressible viscous fluids (76D05) Regularity of solutions in optimal control (49N60) Navier-Stokes equations (35Q30) Duality theory (optimization) (49N15) Optimality conditions for minimax problems (49K35)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A variational approach to the Navier-Stokes equations
- An inverse function theorem in Fréchet spaces
- The pullback equation for differential forms
- A polyconvex integrand; Euler-Lagrange equations and uniqueness of equilibrium
- Energy minimizers in nonlinear elastostatics and the implicit function theorem
- Non-uniqueness of minimizers for strictly polyconvex functionals
- Ordinary differential equations, transport theory and Sobolev spaces
- Differentiability of Lipschitz functions on Banach spaces
- Solutions for semilinear parabolic equations in \(L^ p\) and regularity of weak solutions of the Navier-Stokes system
- Solutions in \(L_ r\) of the Navier-Stokes initial value problem
- Rearrangements of functions, maximization of convex functionals, and vortex rings
- Quasiconvexity and partial regularity in the calculus of variations
- A regularity theorem for minimizers of quasiconvex integrals
- On stability and uniqueness in finite elasticity
- Analyticity of the semigroup generated by the Stokes operator in \(L_r\) spaces
- Convexity conditions and existence theorems in nonlinear elasticity
- Estimates for solutions of nonstationary Navier-Stokes equations
- A combinatorial algorithm for the Euler equations of incompressible flows
- On the \(L^p\) Helmholtz decomposition: a review of a result due to Solonnikov
- On the variational principle
- Generalized resolvent estimates for the Stokes system in bounded and unbounded domains
- Further remarks on the lower semicontinuity of polyconvex integrals
- A note on Aubin-Lions-Dubinskiĭ lemmas
- On the uniqueness of energy minimizers in finite elasticity
- 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
- Weak continuity and lower semicontinuity results for determinants
- Partial regularity for minimizers of singular energy functionals, with application to liquid crystal models
- Some Open Problems in Elasticity
- Maximal functions measuring smoothness
- Connections between optimal transport, combinatorial optimization and hydrodynamics
- Estimates and regularity results for the DiPerna-Lions flow
- Optimal Transport for the System of Isentropic Euler Equations
- Polar factorization and monotone rearrangement of vector‐valued functions
- Elliptic Partial Differential Equations of Second Order
- Uniqueness of non-linear elastic equilibrium for prescribed boundary displacements and sufficiently small strains
- Hidden Convexity in a Problem of Nonlinear Elasticity