American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Liouville-type theorems and universal bounds for nonnegative solutions of the porous medium equation with source
  • DCDS Home
  • This Issue
  • Next Article
    Well-posedness and long-time behaviour for the non-isothermal Cahn-Hilliard equation with memory
April  2010, 26(2): 649-664. doi: 10.3934/dcds.2010.26.649

Wellposedness of the tornado-hurricane equations

Jürgen Saal 1,

1. 

University of Konstanz, Department of Mathematics and Statistics, Box D 187, 78457 Konstanz, Germany

Received  December 2008 Revised  June 2009 Published  October 2009

We prove local-in-time existence of a unique mild solution for the tornado-hurricane equations in a Hilbert space setting. The wellposedness is shown simultaneously in a halfspace, a layer, and a cylinder and for various types of boundary conditions which admit discontinuities at the edges of the cylinder. By an approach based on symmetric forms we first prove maximal regularity for a linearized system. An application of the contraction mapping principle then yields the existence of a unique local-in-time mild solution.
Keywords: cyclones., Weakly compressible Navier-Stokes equations, wellposedness.
Mathematics Subject Classification: Primary: 76D05, 76E07 ; Secondary: 35K2.
Citation: Jürgen Saal. Wellposedness of the tornado-hurricane equations. Discrete and Continuous Dynamical Systems, 2010, 26 (2) : 649-664. doi: 10.3934/dcds.2010.26.649
[1]

Pavel I. Plotnikov, Jan Sokolowski. Compressible Navier-Stokes equations. Conference Publications, 2009, 2009 (Special) : 602-611. doi: 10.3934/proc.2009.2009.602
[2]

Hi Jun Choe, Bataa Lkhagvasuren, Minsuk Yang. Wellposedness of the Keller-Segel Navier-Stokes equations in the critical Besov spaces. Communications on Pure and Applied Analysis, 2015, 14 (6) : 2453-2464. doi: 10.3934/cpaa.2015.14.2453
[3]

Yoshihiro Shibata. On the local wellposedness of free boundary problem for the Navier-Stokes equations in an exterior domain. Communications on Pure and Applied Analysis, 2018, 17 (4) : 1681-1721. doi: 10.3934/cpaa.2018081
[4]

Daoyuan Fang, Ting Zhang. Compressible Navier-Stokes equations with vacuum state in one dimension. Communications on Pure and Applied Analysis, 2004, 3 (4) : 675-694. doi: 10.3934/cpaa.2004.3.675
[5]

Jing Wang, Lining Tong. Stability of boundary layers for the inflow compressible Navier-Stokes equations. Discrete and Continuous Dynamical Systems - B, 2012, 17 (7) : 2595-2613. doi: 10.3934/dcdsb.2012.17.2595
[6]

Misha Perepelitsa. An ill-posed problem for the Navier-Stokes equations for compressible flows. Discrete and Continuous Dynamical Systems, 2010, 26 (2) : 609-623. doi: 10.3934/dcds.2010.26.609
[7]

Peixin Zhang, Jianwen Zhang, Junning Zhao. On the global existence of classical solutions for compressible Navier-Stokes equations with vacuum. Discrete and Continuous Dynamical Systems, 2016, 36 (2) : 1085-1103. doi: 10.3934/dcds.2016.36.1085
[8]

Dong Li, Xinwei Yu. On some Liouville type theorems for the compressible Navier-Stokes equations. Discrete and Continuous Dynamical Systems, 2014, 34 (11) : 4719-4733. doi: 10.3934/dcds.2014.34.4719
[9]

Zhilei Liang. Convergence rate of solutions to the contact discontinuity for the compressible Navier-Stokes equations. Communications on Pure and Applied Analysis, 2013, 12 (5) : 1907-1926. doi: 10.3934/cpaa.2013.12.1907
[10]

Matthew Paddick. The strong inviscid limit of the isentropic compressible Navier-Stokes equations with Navier boundary conditions. Discrete and Continuous Dynamical Systems, 2016, 36 (5) : 2673-2709. doi: 10.3934/dcds.2016.36.2673
[11]

Jan W. Cholewa, Tomasz Dlotko. Fractional Navier-Stokes equations. Discrete and Continuous Dynamical Systems - B, 2018, 23 (8) : 2967-2988. doi: 10.3934/dcdsb.2017149
[12]

Feimin Huang, Xiaoding Shi, Yi Wang. Stability of viscous shock wave for compressible Navier-Stokes equations with free boundary. Kinetic and Related Models, 2010, 3 (3) : 409-425. doi: 10.3934/krm.2010.3.409
[13]

Bingkang Huang, Lusheng Wang, Qinghua Xiao. Global nonlinear stability of rarefaction waves for compressible Navier-Stokes equations with temperature and density dependent transport coefficients. Kinetic and Related Models, 2016, 9 (3) : 469-514. doi: 10.3934/krm.2016004
[14]

Xulong Qin, Zheng-An Yao, Hongxing Zhao. One dimensional compressible Navier-Stokes equations with density-dependent viscosity and free boundaries. Communications on Pure and Applied Analysis, 2008, 7 (2) : 373-381. doi: 10.3934/cpaa.2008.7.373
[15]

Zilai Li, Zhenhua Guo. On free boundary problem for compressible navier-stokes equations with temperature-dependent heat conductivity. Discrete and Continuous Dynamical Systems - B, 2017, 22 (10) : 3903-3919. doi: 10.3934/dcdsb.2017201
[16]

Tao Wang, Huijiang Zhao, Qingyang Zou. One-dimensional compressible Navier-Stokes equations with large density oscillation. Kinetic and Related Models, 2013, 6 (3) : 649-670. doi: 10.3934/krm.2013.6.649
[17]

Ansgar Jüngel, Josipa-Pina Milišić. Full compressible Navier-Stokes equations for quantum fluids: Derivation and numerical solution. Kinetic and Related Models, 2011, 4 (3) : 785-807. doi: 10.3934/krm.2011.4.785
[18]

Yuming Qin, Lan Huang, Zhiyong Ma. Global existence and exponential stability in $H^4$ for the nonlinear compressible Navier-Stokes equations. Communications on Pure and Applied Analysis, 2009, 8 (6) : 1991-2012. doi: 10.3934/cpaa.2009.8.1991
[19]

Xulong Qin, Zheng-An Yao. Global solutions of the free boundary problem for the compressible Navier-Stokes equations with density-dependent viscosity. Communications on Pure and Applied Analysis, 2010, 9 (4) : 1041-1052. doi: 10.3934/cpaa.2010.9.1041
[20]

Ruihong Ji, Yongfu Wang. Mass concentration phenomenon to the 2D Cauchy problem of the compressible Navier-Stokes equations. Discrete and Continuous Dynamical Systems, 2019, 39 (2) : 1117-1133. doi: 10.3934/dcds.2019047

2020 Impact Factor: 1.392

Tools

Metrics

  • PDF downloads (84)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy