Local well-posedness for hyperbolic–elliptic Ishimori equation
Copyright policy )Local well-posedness for hyperbolic–elliptic Ishimori equation
In this paper we consider the hyperbolic-elliptic Ishimori initial-value problem. We prove that such system is locally well-posed for small data in $H^{s}$ level space, for $s> 3/2$. The new ingredient is that we develop the methods of Ionescu and Kenig \cite{IK} and \cite{IK2} to approach the problem in a perturbative way.
30 pages
- North China Electric Power University China (People's Republic of)
local well-posedness, Initial-boundary value problems for mixed-type systems of PDEs, hyperbolic-elliptic system, Hyperbolic–elliptic Ishimori equation, Mathematics - Analysis of PDEs, FOS: Mathematics, Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs, initial value problem, Local well-posedness, Ishimori equation, Analysis, Analysis of PDEs (math.AP)
local well-posedness, Initial-boundary value problems for mixed-type systems of PDEs, hyperbolic-elliptic system, Hyperbolic–elliptic Ishimori equation, Mathematics - Analysis of PDEs, FOS: Mathematics, Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs, initial value problem, Local well-posedness, Ishimori equation, Analysis, Analysis of PDEs (math.AP)
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