Blowup Phenomena for the Compressible Euler and Euler-Poisson Equations with Initial Functional Conditions
We study, in the radial symmetric case, the finite time life span of the compressible Euler or Euler-Poisson equations in RN. For time t≥0, we can define a functional H(t) associated with the solution of the equations and some testing function f. When the pressure function P of the governing equatio...
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/580871 |
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| author | Sen Wong Manwai Yuen |
| author_facet | Sen Wong Manwai Yuen |
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| collection | DOAJ |
| description | We study, in the radial symmetric case, the finite time life span of the compressible Euler or Euler-Poisson equations in RN. For time t≥0, we can define a functional H(t) associated with the solution of the equations and some testing function f. When the pressure function P of the governing equations is of the form P=Kργ, where ρ is the density function, K is a constant, and γ>1, we can show that the nontrivial C1 solutions with nonslip boundary condition will blow up in finite time if H(0) satisfies some initial functional conditions defined by the integrals of f. Examples of the testing functions include rN-1ln(r+1), rN-1er, rN-1(r3-3r2+3r+ε), rN-1sin((π/2)(r/R)), and rN-1sinh r. The corresponding blowup result for the 1-dimensional nonradial symmetric case is also given. |
| format | Article |
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| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-7cc9abaeae944bbb8e44ee7561ddc2d62025-02-03T01:30:45ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/580871580871Blowup Phenomena for the Compressible Euler and Euler-Poisson Equations with Initial Functional ConditionsSen Wong0Manwai Yuen1Department of Mathematics and Information Technology, The Hong Kong Institute of Education, 10 Lo Ping Road, Tai Po, New Territories, Hong KongDepartment of Mathematics and Information Technology, The Hong Kong Institute of Education, 10 Lo Ping Road, Tai Po, New Territories, Hong KongWe study, in the radial symmetric case, the finite time life span of the compressible Euler or Euler-Poisson equations in RN. For time t≥0, we can define a functional H(t) associated with the solution of the equations and some testing function f. When the pressure function P of the governing equations is of the form P=Kργ, where ρ is the density function, K is a constant, and γ>1, we can show that the nontrivial C1 solutions with nonslip boundary condition will blow up in finite time if H(0) satisfies some initial functional conditions defined by the integrals of f. Examples of the testing functions include rN-1ln(r+1), rN-1er, rN-1(r3-3r2+3r+ε), rN-1sin((π/2)(r/R)), and rN-1sinh r. The corresponding blowup result for the 1-dimensional nonradial symmetric case is also given.http://dx.doi.org/10.1155/2014/580871 |
| spellingShingle | Sen Wong Manwai Yuen Blowup Phenomena for the Compressible Euler and Euler-Poisson Equations with Initial Functional Conditions The Scientific World Journal |
| title | Blowup Phenomena for the Compressible Euler and Euler-Poisson Equations with Initial Functional Conditions |
| title_full | Blowup Phenomena for the Compressible Euler and Euler-Poisson Equations with Initial Functional Conditions |
| title_fullStr | Blowup Phenomena for the Compressible Euler and Euler-Poisson Equations with Initial Functional Conditions |
| title_full_unstemmed | Blowup Phenomena for the Compressible Euler and Euler-Poisson Equations with Initial Functional Conditions |
| title_short | Blowup Phenomena for the Compressible Euler and Euler-Poisson Equations with Initial Functional Conditions |
| title_sort | blowup phenomena for the compressible euler and euler poisson equations with initial functional conditions |
| url | http://dx.doi.org/10.1155/2014/580871 |
| work_keys_str_mv | AT senwong blowupphenomenaforthecompressibleeulerandeulerpoissonequationswithinitialfunctionalconditions AT manwaiyuen blowupphenomenaforthecompressibleeulerandeulerpoissonequationswithinitialfunctionalconditions |