Low regularity well-posedness of the Dirac-Klein-Gordon equations in one space dimension [PDF]
arXiv, 2006 We extend recent results of S. Machihara and H. Pecher on low regularity well-posedness of the Dirac-Klein-Gordon (DKG) system in one dimension. Our proof, like that of Pecher, relies on the null structure of DKG, recently completed by D'Ancona, Foschi and Selberg, but we show that in 1d the argument can be simplified by modifying the choice of ...
arxiv
Modified low regularity well-posedness for the one-dimensional Dirac-Klein-Gordon system [PDF]
arXiv, 2007 The 1D Cauchy problem for the Dirac-Klein-Gordon system is shown to be locally well-posed for low regularity Dirac data in $\hat{H^{s,p}}$ and wave data in $\hat{H^{r,p}} \times \hat{H^{r-1,p}}$ for $1
arxiv
Low regularity global well-posedness for the two-dimensional Zakharov system [PDF]
arXiv, 2008 The two-dimensional Zakharov system is shown to have a unique global solution for data without finite energy if the L^2 - norm of the Schr\"odinger part is small enough. The proof uses a refined I-method originally initiated by Colliander, Keel, Staffilani, Takaoka and Tao. A polynomial growth bound for the solution is also given.
arxiv
Unconditional uniqueness in the charge class for the Dirac-Klein-Gordon equations in two space dimensions [PDF]
arXiv, 2011 Recently, A. Gruenrock and H. Pecher proved global well-posedness of the 2d Dirac-Klein-Gordon equations given initial data for the spinor and scalar fields in $H^s$ and $H^{s+1/2} \times H^{s-1/2}$, respectively, where $s\ge 0$, but uniqueness was only known in a contraction space of Bourgain type, strictly smaller than the natural solution space $C ...
arxiv
Unconditional global well-posedness for the 3D Gross-Pitaevskii equation for data without finite energy [PDF]
arXiv, 2012 The Cauchy problem for the Gross-Pitaevskii equation in three space dimensions is shown to have an unconditionally unique global solution for data of the form 1 + H^s for 5/6 < s < 1, which do not have necessarily finite energy. The proof uses the I-method which is complicated by the fact that no L^2 -conservation law holds.
arxiv
Molecules, 2018 Thiopurines (TP) represent an important therapeutic tool for the treatment of inflammatory bowel diseases (IBD) in the current situation of rising incidence and health care costs.
Daniel Pecher +6 more
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Global rough solutions for the Zakharov system in two spatial dimensions [PDF]
arXiv, 2012 We show an improved global well-posedness result for the Zakharov system in two space dimensions with minimal regularity assumptions for the data. Especially we are able to allow Schroedinger and wave data, which do not belong to H^1 and L^2, respectively, thus with infinite energy.
arxiv
Low regularity local well-posedness for the Maxwell-Klein-Gordon equations in Lorenz gauge [PDF]
arXiv, 2013 The Cauchy problem for the Maxwell-Klein-Gordon equations in Lorenz gauge in two and three space dimensions is locally well-posed for low regularity data without finite energy. The result relies on the null structure for the main bilinear terms which was shown to be not only present in Coulomb gauge but also in Lorenz gauge by Selberg and Tesfahun, who
arxiv
Low regularity local well-posedness for the Chern-Simons-Higgs system in temporal gauge [PDF]
arXiv, 2013 The Cauchy problem for the Chern-Simons-Higgs system in the (2+1)-dimensional Minkowski space in temporal gauge is locally well-posed for low regularity initial data improving a result of Huh. The proof uses the bilinear space-time estimates in wave-Sobolev spaces by d'Ancona, Foschi and Selberg and takes advantage of a null condition.
arxiv
Global well-posedness in energy space for the Chern-Simons-Higgs system in temporal gauge [PDF]
arXiv, 2015 The Cauchy problem for the Chern-Simons-Higgs system in the (2+1)-dimensional Minkowski space in temporal gauge is globally well-posed in energy space improving a result of Huh. The proof uses the bilinear space-time estimates in wave-Sobolev spaces by d'Ancona, Foschi and Selberg, an $L^6_x L^2_t$-estimate for solutions of the wave equation, and also ...
arxiv