Blowup of smooth solutions for relativistic Euler equations TeX Export

@misc{citeulike:144019, abstract = {We study the singularity formation of smooth solutions of the relativistic Euler equations in \$(3+1)\$-dimensional spacetime for both finite initial energy and infinite initial energy. For the finite initial energy case, we prove that any smooth solution, with compactly supported non-trivial initial data, blows up in finite time. For the case of infinite initial energy, we first prove the existence, uniqueness and stability of a smooth solution if the initial data is in the subluminal region away from the vacuum. By further assuming the initial data is a smooth compactly supported perturbation around a non-vacuum constant background, we prove the property of finite propagation speed of such a perturbation. The smooth solution is shown to blow up in finite time provided that the radial component of the initial "generalized" momentum is sufficiently large.}, archivePrefix = {arXiv}, author = {Pan, Ronghua and Smoller, Joel A.}, citeulike-article-id = {144019}, citeulike-linkout-0 = {http://arxiv.org/abs/gr-qc/0503080}, citeulike-linkout-1 = {http://arxiv.org/pdf/gr-qc/0503080}, eprint = {gr-qc/0503080}, keywords = {blow-up, euler, gr}, month = {March}, posted-at = {2005-04-01 07:47:07}, priority = {2}, title = {Blowup of smooth solutions for relativistic Euler equations}, url = {http://arxiv.org/abs/gr-qc/0503080}, year = {2005} }

TY - ELEC ID - citeulike:144019 L3 - citeulike-article-id:144019 N2 - We study the singularity formation of smooth solutions of the relativistic Euler equations in $(3+1)$-dimensional spacetime for both finite initial energy and infinite initial energy. For the finite initial energy case, we prove that any smooth solution, with compactly supported non-trivial initial data, blows up in finite time. For the case of infinite initial energy, we first prove the existence, uniqueness and stability of a smooth solution if the initial data is in the subluminal region away from the vacuum. By further assuming the initial data is a smooth compactly supported perturbation around a non-vacuum constant background, we prove the property of finite propagation speed of such a perturbation. The smooth solution is shown to blow up in finite time provided that the radial component of the initial "generalized" momentum is sufficiently large. TI - Blowup of smooth solutions for relativistic Euler equations KW - blow-up KW - euler KW - gr AU - Pan, Ronghua AU - Smoller, Joel PY - 2005/03/18/ UR - http://arxiv.org/abs/gr-qc/0503080 ER -