The asymptotic behavior of periodic solutions to fractal nonlinear Burgers equation is considered and the initial data are allowed to be arbitrarily large.The exponential decay estimates of the solutions are obtained ...The asymptotic behavior of periodic solutions to fractal nonlinear Burgers equation is considered and the initial data are allowed to be arbitrarily large.The exponential decay estimates of the solutions are obtained for the power of Laplacian α∈[1/2,1).展开更多
We study the Cauchy problem of a two-species chemotactic model. Using the Fourier frequency localization and the Bony paraproduct decomposition, we establish a unique local solution and blow-up criterion of the soluti...We study the Cauchy problem of a two-species chemotactic model. Using the Fourier frequency localization and the Bony paraproduct decomposition, we establish a unique local solution and blow-up criterion of the solution, when the initial data（u0, v0, w0） belongs to homogeneous Besov spaces B^˙p,1^-2＋3/p（R^3） ×B^˙r,1^-2＋3/r（R^3） ×B^˙q,1^3/q（R^3） for p, q and r satisfying some technical assumptions. Furthermore, we prove that if the initial data is sufficiently small, then the solution is global. Meanwhile, based on the so-called Gevrey estimates, we particularly prove that the solution is analytic in the spatial variable. In addition, we analyze the long time behavior of the solution and obtain some decay estimates for higher derivatives in Besov and Lebesgue spaces.展开更多
基金Supported by the National Natural Science Foundation of China(11461074)the Program for Young and Middle-aged Leading Talents in Scientific and Technological Innovation of Jilin Province(20200301053RQ)。
基金Supported by the Education Department of Jilin Province of China(JJKH20220527KJ)the Program for Young and Middle-aged Leading Talents in Scientific and Technological Innovation of Jilin Province(20200301053RQ)。
基金Project supported by the National Natural Science Foundation of China (No. 11071162)the Shanghai Jiao Tong University Innovation Fund for Postgraduates (No. WS3220507101)
文摘The asymptotic behavior of periodic solutions to fractal nonlinear Burgers equation is considered and the initial data are allowed to be arbitrarily large.The exponential decay estimates of the solutions are obtained for the power of Laplacian α∈[1/2,1).
基金supported by National Natural Science Foundation of China (Grant Nos. 11671185, 11301248 and 11271175)
文摘We study the Cauchy problem of a two-species chemotactic model. Using the Fourier frequency localization and the Bony paraproduct decomposition, we establish a unique local solution and blow-up criterion of the solution, when the initial data（u0, v0, w0） belongs to homogeneous Besov spaces B^˙p,1^-2＋3/p（R^3） ×B^˙r,1^-2＋3/r（R^3） ×B^˙q,1^3/q（R^3） for p, q and r satisfying some technical assumptions. Furthermore, we prove that if the initial data is sufficiently small, then the solution is global. Meanwhile, based on the so-called Gevrey estimates, we particularly prove that the solution is analytic in the spatial variable. In addition, we analyze the long time behavior of the solution and obtain some decay estimates for higher derivatives in Besov and Lebesgue spaces.
