7 papers
Blowup of smooth solutions to 2D quasilinear wave equations with higher-order null conditions and short pulse initial data
Bingbing Ding, Zhouping Xin, Huicheng Yin
This paper investigates the 2D quasilinear wave equation with the short pulse initial data $(ϕ, \partial_tϕ)|_{…
Shock formation for 3D steady supersonic flows with general short pulse data
Bingbing Ding, Zhouping Xin, Huicheng Yin
This paper concerns the shock formation problem for the 3D steady supersonic potential equation of polytropic gases. The potential equation is described by a second order quasiline…
The sharp lifespan of small data smooth solutions to 2-D quadratic quasilinear wave equations in exterior domains
Bingbing Ding, Fei Hou, Huicheng Yin
In the paper [M. Keel, H. Smith, C.D. Sogge, Almost global existence for quasilinear wave equations in three space dimensions. J. Amer. Math. Soc. 17 (2004), no. 1, 109-153], the a…
Global smooth solutions of 2-D quadratically quasilinear wave equations with null conditions in exterior domains, II
Fei Hou, Huicheng Yin
In the paper [S. Alinhac, The null condition for quasilinear wave equations in two space dimensions I, Invent. Math. 145 (2001), no. 3, 597-618], S. Alinhac established the global…
Global smooth solutions of 2-D quadratic quasilinear wave equations with null conditions in exterior domains
Fei Hou, Huicheng Yin, Meng Yuan
For 3-D quadratic quasilinear wave equations with or without null conditions in exterior domains, when the compatible initial data and Dirichlet boundary values are given, the glob…
Global smooth solutions of 2D quasilinear wave equations with higher order null conditions and short pulse initial data
Bingbing Ding, Zhouping Xin, Huicheng Yin
For the short pulse initial data with a first order outgoing constraint condition and optimal orders of smallness, we establish the global existence of smooth solutions to 2D quasi…
Global smooth solutions of 3-D quasilinear wave equations with small initial data
Ding Bingbing, Liu Yingbo, Yin Huicheng
In this paper, we are concerned with the 3-D quasilinear wave equation $ \ds\sum_{i,j=0}^3g^{ij}(u, \p u)\p_{ij}^2u$ with $(u(0,x), \p_tu(0,x))=(\ve u_0(x), \ve u_1(x))$, wher…