KdV-type equations in projective Gevrey spaces
DOI10.1016/j.matpur.2023.07.007zbMath1527.35342arXiv2212.10530OpenAlexW4385462153MaRDI QIDQ6049051
Alexandre Arias Junior, Alessia Ascanelli, Marco Cappiello
Publication date: 15 September 2023
Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2212.10530
Smoothness and regularity of solutions to PDEs (35B65) Pseudodifferential operators as generalizations of partial differential operators (35S05) PDEs in connection with fluid mechanics (35Q35) KdV equations (Korteweg-de Vries equations) (35Q53) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Liquid-gas two-phase flows, bubbly flows (76T10) Topological linear spaces of test functions, distributions and ultradistributions (46F05) Initial value problems for linear higher-order PDEs (35G10) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Semilinear \(p\)-evolution equations in Sobolev spaces
- Well-posedness of the Cauchy problem for \(p\)-evolution equations
- Gevrey regularity of the periodic gKdV equation
- Some remarks on the Cauchy problem
- The global Cauchy problem for a vibrating beam equation
- Microhyperbolic operators in Gevrey classes
- Parametrix of infinite order on Gevrey spaces to the Cauchy problem for hyperbolic operators with one constant multiple characteristic
- The hyperbolic Cauchy problem
- Exact solutions to the KdV--Burgers' equation
- A necessary condition for \(H^\infty \) well-posedness of \(p\)-evolution equations
- Resolution of singularities in Denjoy-Carleman classes
- The Cauchy problem for Schrödinger type equations
- Gevrey regularizing effect for the (generalized) Korteweg-de Vries equation and nonlinear Schrödinger equations
- The Cauchy problem for 3-evolution equations with data in Gelfand-Shilov spaces
- The Cauchy problem of a periodic higher order KdV equation in analytic Gevrey spaces
- Schrödinger-type equations in Gelfand-Shilov spaces
- Hölder continuity in time for SG hyperbolic systems
- Well-posedness for degenerate Schrödinger equations
- Remarks on pseudo-differential operators
- Pseudodifferential operators of infinite order and Gevrey classes
- The inverse function theorem of Nash and Moser
- On positivity of pseudo-differential operators
- Local existence for semilinear weakly hyperbolic equations with time dependent coefficients
- Gevrey Regularity of the Global Attractor for Damped Forced KdV Equation on the Real Line
- A non-linear equation incorporating damping and dispersion
- On the generalized Korteweg-deVries equation
- Introduction to nonlinear dispersive equations
- Nonlinear hyperbolic Cauchy problems in Gevrey classes
