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Ill-posedness of the quasilinear wave equation in the space $H^7/4 (ln H)^-Béta$ in dimension 2+1

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A vector field method on the distorted Fourier side and decay for wave equations with potentials

Joachim Krieger, Roland Donninger

We study the Cauchy problem for the one-dimensional wave equation

\partial_t^2 u(t,x)-\partial_x^2 u(t,x)+V(x)u(t,x)=0.

The potential

V

is assumed to be smooth with asymptotic behavior

V(x)\sim -\tfrac14 |x|^{-2}\mbox{ as } |x|\to \infty.

...

2016

Ill-posedness of the quasilinear wave equation in the space $H^7/4 (ln H)^-Béta$ in dimension 2+1

Graph Chatbot

Chattez avec Graph Search

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A vector field method on the distorted Fourier side and decay for wave equations with potentials

MATHICSE Technical Report : Multiscale methods for wave problems in heterogeneous media

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Multiplicity Of Solutions For Linear Partial Differential Equations Using (Generalized) Energy Operators

Conservative Model Order Reduction for Fluid Flow

Effective models and numerical homogenization methods for long time wave propagation in heterogeneous media

Multiscale methods for wave problems in heterogenous media

Dynamical Low Rank approximation of PDEs with random parameters

IGS: an IsoGeometric approach for Smoothing on surfaces

MATHICSE Technical Report : Multiscale methods for wave problems in heterogeneous media

Existence and Non-uniqueness of Global Weak Solutions to Inviscid Primitive and Boussinesq Equations

Particle-size and -density segregation in granular free-surface flows

A vector field method on the distorted Fourier side and decay for wave equations with potentials