Unconditional Uniqueness of 5th Order KP Equations

2025/08/27 by Patterson, James
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.19779

Abstract

In this paper we study the 5th Order Kadomstev-Petviashvili (KP) equations posed on the real line. In particular we adapt the energy estimate argument from Guo-Molinet (arXiv:2404.12364v1 [math.AP]) to conclude unconditional uniqueness of the solution to data map for 5th order KP type equations. Applying short-time X^s,b methods to improve classical energy estimates provides more than sufficient decay when considering estimates on the interior of the time interval [0,T]. The issue is how we deal with the boundary. By abusing symmetry we can apply multilinear interpolation to gain access to L⁴ Strichartz estimates, which provide improved derivative gain. When taken together, the regularity of our resultant function space can be arbitrarily close to L², which in the context of unconditional uniqueness results is almost sharp.

Citations

• On the well-posedness of the KP-I equation
• Unconditional uniqueness of solutions for nonlinear dispersive equations
• Normal form approach to the one-dimensional periodic cubic nonlinear Schrödinger equation in almost critical Fourier-Lebesgue spaces
• Normal form approach to unconditional well-posedness of nonlinear dispersive PDEs on the real line
• On unconditional well-posedness of modified KdV
• On the local regularity of the KP-I equation in anisotropic Sobolev space
• Well-posedness for the Kadomtsev-Petviashvili II equation and generalisations
• On nonlinear Schrödinger equations, II.H S -solutions and unconditional well-posedness

Related

• Rough solutions of the fifth-order KdV equations
• Well-posedness for the fifth-order KdV equation in the energy space
• Local well-posedness for the fifth-order KdV equations on \mathbbT
• Unconditional uniqueness for the modified Korteweg-de Vries equation on the line
• On the Cauchy problem for the periodic fifth-order KP-I equation