Gevrey well posedness for a second order weakly hyperbolic equation with non regular in time coefficients

Well-posedness of Second Order Evolution Equation on Discrete Time

We characterize the well-posedness for second order discrete evolution equations in UMD spaces by means of Fourier multipliers and R-boundedness properties of the resolvent operator which defines the equation. Applications to semilinear problems are given.

Almost global well-posedness of Kirchhoff equation with Gevrey data

Article history: Received 26 November 2016 Accepted after revision 3 April 2017 Available online 18 April 2017 Presented by the Editorial Board The aim of this note is to present the almost global well-posedness result for the Cauchy problem for the Kirchhoff equation with large data in Gevrey spaces. We also briefly discuss the corresponding results in bounded and in exterior domains. © 2017 A...

Local Well-posedness for Hyperbolic-elliptic Ishimori Equation

In this paper we consider the hyperbolic-elliptic Ishimori initial-value problem with the form:    ∂ts = s× xs+ b(φx1sx2 + φx2sx1) on R 2 × [−1, 1]; ∆φ = 2s · (sx1 × sx2) s(0) = s0 where s(·, t) : R → S ⊂ R, × denotes the wedge product in R, x = ∂ x1 −∂ 2 x2 , b ∈ R. We prove that such system is locally well-posed for small data s0 ∈ H0 Q (R ; S), σ0 > 3/2, Q ∈ S. The new ingredient is that ...

Well-posedness for Hyperbolic Problems

Well-posedness for a Higher-order Benjamin-ono Equation

In this paper we prove that the initial value problem associated to the following higher-order Benjamin-Ono equation ∂tv − bH∂ xv + a∂ xv = cv∂xv − d∂x(vH∂xv + H(v∂xv)), where x, t ∈ R, v is a real-valued function, H is the Hilbert transform, a ∈ R, b, c and d are positive constants, is locally well-posed for initial data v(0) = v0 ∈ H(R), s ≥ 2 or v0 ∈ H(R) ∩ L(R; xdx), k ∈ Z+, k ≥ 2.