Global Strong Solutions to Cauchy Problem of 1D Non-resistive MHD Equations with No Vacuum at Infinity
In this paper, we study the Cauchy problem of 1D non-resistive compressible magnetohydrodynamics (MHD) equations. We established the global existence and uniqueness of strong solutions for large initial data, where the initial density and initial magnetic field approach non-zero constants at infinit...
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| Veröffentlicht in: | Acta applicandae mathematicae 2021-10, Vol.175 (1), Article 7 |
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| creator | Ai, Xiaolian Li, Zilai Ye, Yulin |
| description | In this paper, we study the Cauchy problem of 1D non-resistive compressible magnetohydrodynamics (MHD) equations. We established the global existence and uniqueness of strong solutions for large initial data, where the initial density and initial magnetic field approach non-zero constants at infinity, but the initial vacuum of the density inside the region can be permitted. The analysis is based on the Caffarelli-Kohn-Nirenberg weighted inequality and the technique of mathematical frequency decomposition to get the upper bound of the density, and no more artificial conditions are needed to obtain the upper bound estimate of magnetic field
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| doi_str_mv | 10.1007/s10440-021-00434-1 |
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Xiaolian</au><au>Li, Zilai</au><au>Ye, Yulin</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Global Strong Solutions to Cauchy Problem of 1D Non-resistive MHD Equations with No Vacuum at Infinity</atitle><jtitle>Acta applicandae mathematicae</jtitle><stitle>Acta Appl Math</stitle><date>2021-10-01</date><risdate>2021</risdate><volume>175</volume><issue>1</issue><artnum>7</artnum><issn>0167-8019</issn><eissn>1572-9036</eissn><abstract>In this paper, we study the Cauchy problem of 1D non-resistive compressible magnetohydrodynamics (MHD) equations. We established the global existence and uniqueness of strong solutions for large initial data, where the initial density and initial magnetic field approach non-zero constants at infinity, but the initial vacuum of the density inside the region can be permitted. The analysis is based on the Caffarelli-Kohn-Nirenberg weighted inequality and the technique of mathematical frequency decomposition to get the upper bound of the density, and no more artificial conditions are needed to obtain the upper bound estimate of magnetic field
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| subjects | Applications of Mathematics Calculus of Variations and Optimal Control Optimization Cauchy problems Compressibility Computational Mathematics and Numerical Analysis Density Infinity Magnetic fields Magnetohydrodynamics Mathematical analysis Mathematics Mathematics and Statistics Partial Differential Equations Probability Theory and Stochastic Processes Upper bounds |
| title | Global Strong Solutions to Cauchy Problem of 1D Non-resistive MHD Equations with No Vacuum at Infinity |
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