Decoupling inequality for paraboloid under shell type restriction and its application to the periodic Zakharov system

DOI10.1007/s00220-023-04852-0zbMath1528.35148arXiv2212.01805MaRDI QIDQ6067737

Akansha Sanwal, Shinya Kinoshita, Shohei Nakamura

Publication date: 17 November 2023

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2212.01805

zbMATH Keywords

Zakharov system

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) KdV equations (Korteweg-de Vries equations) (35Q53) NLS equations (nonlinear Schrödinger equations) (35Q55) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Statistical mechanics of plasmas (82D10) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Cites Work

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• Proof of the main conjecture in Vinogradov's mean value theorem for degrees higher than three
• Local well-posedness for the Zakharov system on the multidimensional torus
• On the cone multiplier in \(\mathbb R^3\)
• A study guide for the \(l^{2}\) decoupling theorem
• Convolutions of singular measures and applications to the Zakharov system
• Bounds on oscillatory integral operators based on multilinear estimates
• Decouplings for three-dimensional surfaces in \(\mathbb{R}^{6}\)
• Some nonlinear Brascamp-Lieb inequalities and applications to harmonic analysis
• Wolff's inequality for hypersurfaces
• On the multilinear restriction and Kakeya conjectures
• Well-posedness and scattering for the Zakharov system in four dimensions
• A convolution estimate for two-dimensional hypersurfaces
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
• Existence and smoothing effect of solutions for the Zakharov equations
• On the Cauchy and invariant measure problem for the periodic Zakharov system
• Periodic Korteweg-de Vries equation with measures as initial data
• On the Cauchy problem for the Zakharov system
• A local smoothing estimate in higher dimensions.
• Local smoothing type estimates on \(L^p\) for large \(p\)
• On a bilinear Strichartz estimate on irrational tori
• Well-posedness for the Zakharov system with the periodic boundary condition
• Generalized Strichartz inequalities for the wave equation
• Moment inequalities for trigonometric polynomials with spectrum in curved hypersurfaces
• An \(l^2\) decoupling interpretation of efficient congruencing: the parabola
• A note on bilinear wave-Schrödinger interactions
• Local well-posedness for the Zakharov system in dimension \(d = 2, 3\)
• Local well-posedness for the Zakharov system in dimension \(d \leqslant 3\)
• A sharp square function estimate for the cone in \(\mathbb{R}^3\)
• On the nonlinear Brascamp-Lieb inequality
• Global wellposedness for the energy-critical Zakharov system below the ground state
• Multi-scale bilinear restriction estimates for general phases
• The proof of the \(l^2\) decoupling conjecture
• Construction of blow-up solutions for Zakharov system on \(\mathbb T^2\)
• On mappings, conformal at the boundary
• A note on spherical summation multipliers
• A nonlinear generalisation of the Loomis-Whitney inequality and applications
• Aspects of Multilinear Harmonic Analysis Related to Transversality
• Strichartz estimates for Schrödinger equations on irrational tori
• Fourier Integrals in Classical Analysis
• A trilinear approach to square function and local smoothing estimates for the wave operator
• L p regularity of averages over curves and bounds for associated maximal operators
• On the 2D Zakharov system withL²Schrödinger data
• On plate decompositions of cone multipliers
• A bilinear approach to the restriction and Kakeya conjectures
• Endpoint Strichartz estimates
• Space‐time estimates for null forms and the local existence theorem
• Stability of the Brascamp-Lieb constant and applications
• A trilinear restriction problem for the paraboloid in ℝ³
• Strichartz inequalities and the nonlinear Schrodinger equation on compact manifolds
• The Zakharov system in 4D radial energy space below the ground state
• A short proof of ℓ2 decoupling for the moment curve
• Random Data Wave Equations
• The Vinogradov Mean Value Theorem [after Wooley, and Bourgain, Demeter and Guth]
• Decoupling for certain quadratic surfaces of low co‐dimensions
• Fourier Restriction, Decoupling, and Applications
• A short proof of the multilinear Kakeya inequality
• The Zakharov system in dimension \(d \geq 4\)

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