Local well-posedness for incompressible neo-Hookean elastic equations in almost critical Sobolev spaces
DOI10.1007/s00526-024-02681-0arXiv2308.07739OpenAlexW4392558298MaRDI QIDQ6193422
Publication date: 16 March 2024
Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2308.07739
Smoothness and regularity of solutions to PDEs (35B65) Nonlinear elasticity (74B20) Nonlinear waves in solid mechanics (74J30) PDEs with low regular coefficients and/or low regular data (35R05) Existence problems for PDEs: global existence, local existence, non-existence (35A01) PDEs in connection with mechanics of deformable solids (35Q74) Existence, uniqueness, and regularity theory for incompressible inviscid fluids (76B03) Euler equations (35Q31) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)
Cites Work
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- Global existence for the 2D incompressible isotropic elastodynamics for small initial data
- Almost critical well-posedness for nonlinear wave equations with \(Q_{\mu \nu}\) null forms in 2D
- A sharp counterexample to the local existence of low-regularity solutions to nonlinear wave equations
- On the equation \(\square \phi = | \nabla \phi |^2\) in four space dimensions
- On the equation \(\square u=|\nabla u|^2\) in \(5+1\) dimensions
- Concerning ill-posedness for semilinear wave equations
- Strong ill-posedness of the incompressible Euler equation in borderline Sobolev spaces
- Local well-posedness and ill-posedness on the equation of type \(\square u=u^k(\partial u)^\alpha\)
- Cauchy problem for incompressible neo-Hookean materials
- Global Well-Posedness of Incompressible Elastodynamics in Two Dimensions
- Almost global existence for 2-D incompressible isotropic elastodynamics
- ON THE WAVE EQUATION WITH QUADRATIC NONLINEARITIES IN THREE SPACE DIMENSIONS
- Fourier Analysis and Nonlinear Partial Differential Equations
- Commutator estimates and the euler and navier-stokes equations
- Local regularity of nonlinear wave equations in three space dimensions
- Endpoint Strichartz estimates
- Space‐time estimates for null forms and the local existence theorem
- Local existence with minimal regularity for nonlinear wave equations
- Remark on the optimal regularity for equations of wave maps type
- Bilinear space-time estimates for homogeneous wave equations
- BILINEAR ESTIMATES AND APPLICATIONS TO NONLINEAR WAVE EQUATIONS
- Rough solutions for the wave maps equation
- On the well‐posedness of the Euler equations in the Triebel‐Lizorkin spaces
- Counterexamples to Local Existence for Semi-Linear Wave Equations
- Global existence for three‐dimensional incompressible isotropic elastodynamics
- Global regularity of wave maps. II: Small energy in two dimensions
