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New Bilinear Estimates for Quadratic-Derivative Nonlinear Wave Equations in 2+1 Dimensions
Bilinear Estimates Quadratic-Derivative Nonlinear
2014/12/8
This thesis is concerned with the Cauchy problem for the quadratic derivative nonlinear wave equation in two spatial dimensions. Using standard techniques, we reduce local well-posedness in Fourier Le...
Strichartz estimates for Dirichlet-wave equations in two dimensions with applications
Strichartz estimtes Strauss conjecture obstacles
2011/2/21
We establish the Strauss conjecture for nontrapping obstacles when the spatial dimension n is two. As pointed out in [7] this case is more subtle than n = 3 or 4 due to the fact that the arguments of ...
On the classification of scalar evolutionary integrable equations in $2+1$ dimensions
On the classification scalar evolutionary integrable equations $2+1$ dimensions
2010/11/10
We consider evolutionary equations of the form $u_t=F(u, w)$ where $w=D_x^{-1}D_yu$ is the nonlocality, and the right hand side $F$ is polynomial in the derivatives of $u$ and $w$. The recent paper \c...