Cauchy problem for fractional non-autonomous evolution equations [PDF]
Banach Journal of Mathematical Analysis, 2019 This paper deals with the Cauchy problem to a class of nonlinear time fractional non-autonomous integro-differential evolution equation of mixed type via measure of noncompactness in infinite-dimensional Banach spaces.
Pengyu Chen, Xuping Zhang, Yongxiang Li
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The finite-gap method and the periodic NLS Cauchy problem of anomalous waves for a finite number of unstable modes [PDF]
Russian Mathematical Surveys, 2018 The focusing non-linear Schrödinger (NLS) equation is the simplest universal model describing the modulation instability (MI) of quasimonochromatic waves in weakly non-linear media, and MI is considered to be the main physical mechanism for the ...
P. Grinevich +8 more
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The Cauchy Problem for the Fractional Kadomtsev-Petviashvili Equations [PDF]
SIAM Journal on Mathematical Analysis, 2017 The aim of this paper is to prove various ill-posedness and well-posedness results on the Cauchy problem associated to a class of fractional Kadomtsev--Petviashvili (KP) equations, including the KP...
F. Linares, D. Pilod, J. Saut
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Cauchy problem for the Kuznetsov equation [PDF]
Discrete and Continuous Dynamical Systems. Series A, 2017 We consider the Cauchy problem for a model of non-linear acoustics, named the Kuznetsov equation, describing sound propagation in thermo-viscous elastic media.
A. Dekkers, A. Rozanova-Pierrat
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Global existence and large time asymptotic behavior of strong solutions to the Cauchy problem of 2D density-dependent Navier–Stokes equations with vacuum [PDF]
, 2015 We are concerned with the Cauchy problem of the two-dimensional (2D) nonhomogeneous incompressible Navier–Stokes equations with vacuum as far-field density.
Boqiang Lü, Xiaoding Shi, X. Zhong
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Remarks on the Cauchy problem for the axisymmetric Navier-Stokes equations [PDF]
, 2015 Motivated by applications to vortex rings, we study the Cauchy problem for the three-dimensional axisymmetric Navier-Stokes equations without swirl, using scale invariant function spaces.
T. Gallay, V. Sverák
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On strong solutions to the Cauchy problem of the two-dimensional compressible magnetohydrodynamic equations with vacuum [PDF]
, 2015 Two-dimensional barotropic compressible magnetohydrodynamic equations with shear and bulk viscosities being a positive constant and a power function of the density, respectively, are considered.
Boqiang Lv, Bingkang Huang
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Cauchy Problem and Exponential Stability for the Inhomogeneous Landau Equation [PDF]
, 2015 This work deals with the inhomogeneous Landau equation on the torus in the cases of hard, Maxwellian and moderately soft potentials. We first investigate the linearized equation and we prove exponential decay estimates for the associated semigroup.
K. Carrapatoso +2 more
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A Gronwall inequality and the Cauchy-type problem by means of ψ-Hilfer operator [PDF]
Differential Equations & Applications, 2017 In this paper, we propose a generalized Gronwall inequality through the fractional integral with respect to another function. The Cauchy-type problem for a nonlinear differential equation involving the $\psi$-Hilfer fractional derivative and the ...
J. Sousa, E. C. Oliveira
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Journal of Mathematical Analysis and Applications, 1969 AbstractConsider the singular Cauchy problem for the quasi-linear equation ux2muxx − uyy + f(x, y, u(x, y)) = 0, with initial conditions u(x, 0) = 0, uy(x, 0) = ϑ(x), x ϵ I, where m is any positive real number less than 1 and I = [α, β] is a finite closed interval.Using a result of Ogawa (J. Math.
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