May  2009, 8(3): 1117-1132. doi: 10.3934/cpaa.2009.8.1117

$L^2$-concentration phenomenon for Zakharov system below energy norm II

1. 

Department of Mathematics, Zhejiang University, Hangzhou 310027, China

Received  June 2008 Revised  November 2008 Published  February 2009

In this paper, we will prove a $L^2$-concentration result of Zakharov system in space dimension two, with initial data $(u_0,n_0,n_1)\in H^s\times L^2\times H^{-1}$ ($\frac {1 2}{1 3} < s < 1$), when blow up of the solution happens, by resonant decomposition and I-method, which is an improvement of [13].
Citation: Sijia Zhong, Daoyuan Fang. $L^2$-concentration phenomenon for Zakharov system below energy norm II. Communications on Pure and Applied Analysis, 2009, 8 (3) : 1117-1132. doi: 10.3934/cpaa.2009.8.1117
[1]

Jian Zhang, Shihui Zhu, Xiaoguang Li. Rate of $L^2$-concentration of the blow-up solution for critical nonlinear Schrödinger equation with potential. Mathematical Control and Related Fields, 2011, 1 (1) : 119-127. doi: 10.3934/mcrf.2011.1.119

[2]

José R. Quintero, Juan C. Cordero. Instability of the standing waves for a Benney-Roskes/Zakharov-Rubenchik system and blow-up for the Zakharov equations. Discrete and Continuous Dynamical Systems - B, 2020, 25 (4) : 1213-1240. doi: 10.3934/dcdsb.2019217

[3]

P. Blue, J. Colliander. Global well-posedness in Sobolev space implies global existence for weighted $L^2$ initial data for $L^2$-critical NLS. Communications on Pure and Applied Analysis, 2006, 5 (4) : 691-708. doi: 10.3934/cpaa.2006.5.691

[4]

Vural Bayrak, Emil Novruzov, Ibrahim Ozkol. Local-in-space blow-up criteria for two-component nonlinear dispersive wave system. Discrete and Continuous Dynamical Systems, 2019, 39 (10) : 6023-6037. doi: 10.3934/dcds.2019263

[5]

Yi-hang Hao, Xian-Gao Liu. The existence and blow-up criterion of liquid crystals system in critical Besov space. Communications on Pure and Applied Analysis, 2014, 13 (1) : 225-236. doi: 10.3934/cpaa.2014.13.225

[6]

Bin Li. On the blow-up criterion and global existence of a nonlinear PDE system in biological transport networks. Kinetic and Related Models, 2019, 12 (5) : 1131-1162. doi: 10.3934/krm.2019043

[7]

Lili Du, Chunlai Mu, Zhaoyin Xiang. Global existence and blow-up to a reaction-diffusion system with nonlinear memory. Communications on Pure and Applied Analysis, 2005, 4 (4) : 721-733. doi: 10.3934/cpaa.2005.4.721

[8]

Shu-Xiang Huang, Fu-Cai Li, Chun-Hong Xie. Global existence and blow-up of solutions to a nonlocal reaction-diffusion system. Discrete and Continuous Dynamical Systems, 2003, 9 (6) : 1519-1532. doi: 10.3934/dcds.2003.9.1519

[9]

Zijun Chen, Shengkun Wu. Local well-posedness for the Zakharov system in dimension $ d = 2, 3 $. Communications on Pure and Applied Analysis, 2021, 20 (12) : 4307-4319. doi: 10.3934/cpaa.2021161

[10]

Miaoqing Tian, Sining Zheng. Global boundedness versus finite-time blow-up of solutions to a quasilinear fully parabolic Keller-Segel system of two species. Communications on Pure and Applied Analysis, 2016, 15 (1) : 243-260. doi: 10.3934/cpaa.2016.15.243

[11]

Long Wei, Zhijun Qiao, Yang Wang, Shouming Zhou. Conserved quantities, global existence and blow-up for a generalized CH equation. Discrete and Continuous Dynamical Systems, 2017, 37 (3) : 1733-1748. doi: 10.3934/dcds.2017072

[12]

Katrin Grunert. Blow-up for the two-component Camassa--Holm system. Discrete and Continuous Dynamical Systems, 2015, 35 (5) : 2041-2051. doi: 10.3934/dcds.2015.35.2041

[13]

Ning-An Lai, Yi Zhou. Blow up for initial boundary value problem of critical semilinear wave equation in two space dimensions. Communications on Pure and Applied Analysis, 2018, 17 (4) : 1499-1510. doi: 10.3934/cpaa.2018072

[14]

E. Compaan. A note on global existence for the Zakharov system on $ \mathbb{T} $. Communications on Pure and Applied Analysis, 2019, 18 (5) : 2473-2489. doi: 10.3934/cpaa.2019112

[15]

Hengrong Du, Changyou Wang. Global weak solutions to the stochastic Ericksen–Leslie system in dimension two. Discrete and Continuous Dynamical Systems, 2022, 42 (5) : 2175-2197. doi: 10.3934/dcds.2021187

[16]

Youshan Tao, Michael Winkler. Boundedness vs.blow-up in a two-species chemotaxis system with two chemicals. Discrete and Continuous Dynamical Systems - B, 2015, 20 (9) : 3165-3183. doi: 10.3934/dcdsb.2015.20.3165

[17]

Binbin Shi, Weike Wang. Existence and blow up of solutions to the $ 2D $ Burgers equation with supercritical dissipation. Discrete and Continuous Dynamical Systems - B, 2020, 25 (3) : 1169-1192. doi: 10.3934/dcdsb.2019215

[18]

Xiaojing Xu. Local existence and blow-up criterion of the 2-D compressible Boussinesq equations without dissipation terms. Discrete and Continuous Dynamical Systems, 2009, 25 (4) : 1333-1347. doi: 10.3934/dcds.2009.25.1333

[19]

Yukihiro Seki. A remark on blow-up at space infinity. Conference Publications, 2009, 2009 (Special) : 691-696. doi: 10.3934/proc.2009.2009.691

[20]

Ronghua Jiang, Jun Zhou. Blow-up and global existence of solutions to a parabolic equation associated with the fraction p-Laplacian. Communications on Pure and Applied Analysis, 2019, 18 (3) : 1205-1226. doi: 10.3934/cpaa.2019058

2021 Impact Factor: 1.273

Metrics

  • PDF downloads (82)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]