In this paper, under some assumptions on the flow with a low Mach number, we study the nonexistence of a global nontrivial subsonic solution in an unbounded domain Ω which is one part of a 3D ramp. The flow is assume...In this paper, under some assumptions on the flow with a low Mach number, we study the nonexistence of a global nontrivial subsonic solution in an unbounded domain Ω which is one part of a 3D ramp. The flow is assumed to be steady, isentropic and irrotational, namely, the movement of the flow is described by the potential equation. By establishing a fundamental a priori estimate on the solution of a second order linear elliptic equation in Ω with Neumann boundary conditions on Ω and Dirichlet boundary value at some point of Ω, we show that there is no global nontrivial subsonic flow with a low Mach number in such a domain Ω.展开更多
For a special class of quasilinear wave equations with small initial data which satisfy the nondegenerate assumption, the authors prove that the radially symmetric solution develops singularities in the second order d...For a special class of quasilinear wave equations with small initial data which satisfy the nondegenerate assumption, the authors prove that the radially symmetric solution develops singularities in the second order derivatives in finite time while the first order derivatives and the solution itself remain continuous and small. More precisely, it turns out that this solution is a "geometric blowup solution of cusp type", according to the terminology posed by S. Alinhac[2].展开更多
In this paper, we study the lifespan of solutions for three dimensional compressible Euler equations with spherically symmetric initial data that is a small perturbation of amplitude ε from a constant state. From our...In this paper, we study the lifespan of solutions for three dimensional compressible Euler equations with spherically symmetric initial data that is a small perturbation of amplitude ε from a constant state. From our result, the classical solutions have to blow up in finite time in spite of any small ε.展开更多
基金supported by National Basic Research Programm of China (Grant No.2006CB805902)National Natural Science Foundation of China (Grant No. 10871096)
文摘In this paper, under some assumptions on the flow with a low Mach number, we study the nonexistence of a global nontrivial subsonic solution in an unbounded domain Ω which is one part of a 3D ramp. The flow is assumed to be steady, isentropic and irrotational, namely, the movement of the flow is described by the potential equation. By establishing a fundamental a priori estimate on the solution of a second order linear elliptic equation in Ω with Neumann boundary conditions on Ω and Dirichlet boundary value at some point of Ω, we show that there is no global nontrivial subsonic flow with a low Mach number in such a domain Ω.
文摘For a special class of quasilinear wave equations with small initial data which satisfy the nondegenerate assumption, the authors prove that the radially symmetric solution develops singularities in the second order derivatives in finite time while the first order derivatives and the solution itself remain continuous and small. More precisely, it turns out that this solution is a "geometric blowup solution of cusp type", according to the terminology posed by S. Alinhac[2].
基金Project supported by the Tianyuan Foundation of Chinathe National Natural Science Foundation of ChinaLab of Mathematics for Nonlinear Problems. Fudan University
文摘In this paper, we study the lifespan of solutions for three dimensional compressible Euler equations with spherically symmetric initial data that is a small perturbation of amplitude ε from a constant state. From our result, the classical solutions have to blow up in finite time in spite of any small ε.
