Local and global results for wave maps I
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Publication:4220078
DOI10.1080/03605309808821400zbMath0914.35083OpenAlexW2100485936MaRDI QIDQ4220078
Publication date: 17 February 1999
Published in: Communications in Partial Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1080/03605309808821400
Smoothness and regularity of solutions to PDEs (35B65) Second-order nonlinear hyperbolic equations (35L70) Initial value problems for second-order hyperbolic equations (35L15) Hyperbolic equations on manifolds (58J45)
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Cites Work
- Unnamed Item
- On \(L_2-L_{p'}\) estimates for the wave-equation
- Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
- The Cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices
- On the regularity properties of a model problem related to wave maps
- Generalized Strichartz inequalities for the wave equation
- On the regularity of spherically symmetric wave maps
- Weak solutions and development of singularities of the SU(2) σ‐model
- On the optimal local regularity for the Yang-Mills equations in ℝ⁴⁺¹
- Space‐time estimates for null forms and the local existence theorem
- Remark on the optimal regularity for equations of wave maps type
- TheXsθspaces and unique continuation for solutions to the semilinear wave equation
